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Cayley's Matrix Notation


Checking whether or not a node has been previously definedMath notation and FontsDouble vertical bar notation“Where” notation in definitionNotation for multivariate normalWhich “bold” style is recommended for matrix notation?Math notation in LaTeX?Physics notationPercent notationSummation notation with an incrementUsing printeranswers environment, how to print solutions in the box without the title “Solutions”













3















Cayley used the following notation in his original paper
A Memoir on the Theory of Matrices 1



enter image description here



My attempt to reproduce the notation is shown below:



documentclass{article}
usepackage{amsmath,amssymb,graphicx}
begin{document}
scalebox{2.5}{parbox{0.3textwidth}{$$
renewcommandarraystretch{0}setlengtharraycolsep{0pt}
(mathrm{X}, mathrm{Y}, mathrm{Z}){=}lower10pthbox{$begin{array}{r@{}c@{,mkern10mu}c @{,mkern10mu}c@{,mkern10mu}c l}
( &a &b & c & )\
lvert& a' &b' & c' &rvert\
lvert& a'' & b'' & c'' & rvert\
end{array}$}mkern-6mu(x,y,z),
$$}}
end{document}


As you will observe the delimiters need to be improved. Any suggestions?










share|improve this question























  • is it just my eyes or am I right in thinking that on its own the () are symmetric pair but the overlapping )( symbol is using thinner more rounded )( to get more of an overlap so not using the matching parens for the outer borders of the matrices....

    – David Carlisle
    2 hours ago











  • more $(1,2,3between 4,5,6)$ than $(1,2,3)!( 4,5,6)$

    – David Carlisle
    2 hours ago











  • @DavidCarlisle No it is the same thickness. There is a link to the Royal Society paper jstor.org/stable/pdf/108649.pdf

    – Yiannis Lazarides
    2 hours ago
















3















Cayley used the following notation in his original paper
A Memoir on the Theory of Matrices 1



enter image description here



My attempt to reproduce the notation is shown below:



documentclass{article}
usepackage{amsmath,amssymb,graphicx}
begin{document}
scalebox{2.5}{parbox{0.3textwidth}{$$
renewcommandarraystretch{0}setlengtharraycolsep{0pt}
(mathrm{X}, mathrm{Y}, mathrm{Z}){=}lower10pthbox{$begin{array}{r@{}c@{,mkern10mu}c @{,mkern10mu}c@{,mkern10mu}c l}
( &a &b & c & )\
lvert& a' &b' & c' &rvert\
lvert& a'' & b'' & c'' & rvert\
end{array}$}mkern-6mu(x,y,z),
$$}}
end{document}


As you will observe the delimiters need to be improved. Any suggestions?










share|improve this question























  • is it just my eyes or am I right in thinking that on its own the () are symmetric pair but the overlapping )( symbol is using thinner more rounded )( to get more of an overlap so not using the matching parens for the outer borders of the matrices....

    – David Carlisle
    2 hours ago











  • more $(1,2,3between 4,5,6)$ than $(1,2,3)!( 4,5,6)$

    – David Carlisle
    2 hours ago











  • @DavidCarlisle No it is the same thickness. There is a link to the Royal Society paper jstor.org/stable/pdf/108649.pdf

    – Yiannis Lazarides
    2 hours ago














3












3








3


2






Cayley used the following notation in his original paper
A Memoir on the Theory of Matrices 1



enter image description here



My attempt to reproduce the notation is shown below:



documentclass{article}
usepackage{amsmath,amssymb,graphicx}
begin{document}
scalebox{2.5}{parbox{0.3textwidth}{$$
renewcommandarraystretch{0}setlengtharraycolsep{0pt}
(mathrm{X}, mathrm{Y}, mathrm{Z}){=}lower10pthbox{$begin{array}{r@{}c@{,mkern10mu}c @{,mkern10mu}c@{,mkern10mu}c l}
( &a &b & c & )\
lvert& a' &b' & c' &rvert\
lvert& a'' & b'' & c'' & rvert\
end{array}$}mkern-6mu(x,y,z),
$$}}
end{document}


As you will observe the delimiters need to be improved. Any suggestions?










share|improve this question














Cayley used the following notation in his original paper
A Memoir on the Theory of Matrices 1



enter image description here



My attempt to reproduce the notation is shown below:



documentclass{article}
usepackage{amsmath,amssymb,graphicx}
begin{document}
scalebox{2.5}{parbox{0.3textwidth}{$$
renewcommandarraystretch{0}setlengtharraycolsep{0pt}
(mathrm{X}, mathrm{Y}, mathrm{Z}){=}lower10pthbox{$begin{array}{r@{}c@{,mkern10mu}c @{,mkern10mu}c@{,mkern10mu}c l}
( &a &b & c & )\
lvert& a' &b' & c' &rvert\
lvert& a'' & b'' & c'' & rvert\
end{array}$}mkern-6mu(x,y,z),
$$}}
end{document}


As you will observe the delimiters need to be improved. Any suggestions?







math-mode






share|improve this question













share|improve this question











share|improve this question




share|improve this question










asked 2 hours ago









Yiannis LazaridesYiannis Lazarides

93k21235516




93k21235516













  • is it just my eyes or am I right in thinking that on its own the () are symmetric pair but the overlapping )( symbol is using thinner more rounded )( to get more of an overlap so not using the matching parens for the outer borders of the matrices....

    – David Carlisle
    2 hours ago











  • more $(1,2,3between 4,5,6)$ than $(1,2,3)!( 4,5,6)$

    – David Carlisle
    2 hours ago











  • @DavidCarlisle No it is the same thickness. There is a link to the Royal Society paper jstor.org/stable/pdf/108649.pdf

    – Yiannis Lazarides
    2 hours ago



















  • is it just my eyes or am I right in thinking that on its own the () are symmetric pair but the overlapping )( symbol is using thinner more rounded )( to get more of an overlap so not using the matching parens for the outer borders of the matrices....

    – David Carlisle
    2 hours ago











  • more $(1,2,3between 4,5,6)$ than $(1,2,3)!( 4,5,6)$

    – David Carlisle
    2 hours ago











  • @DavidCarlisle No it is the same thickness. There is a link to the Royal Society paper jstor.org/stable/pdf/108649.pdf

    – Yiannis Lazarides
    2 hours ago

















is it just my eyes or am I right in thinking that on its own the () are symmetric pair but the overlapping )( symbol is using thinner more rounded )( to get more of an overlap so not using the matching parens for the outer borders of the matrices....

– David Carlisle
2 hours ago





is it just my eyes or am I right in thinking that on its own the () are symmetric pair but the overlapping )( symbol is using thinner more rounded )( to get more of an overlap so not using the matching parens for the outer borders of the matrices....

– David Carlisle
2 hours ago













more $(1,2,3between 4,5,6)$ than $(1,2,3)!( 4,5,6)$

– David Carlisle
2 hours ago





more $(1,2,3between 4,5,6)$ than $(1,2,3)!( 4,5,6)$

– David Carlisle
2 hours ago













@DavidCarlisle No it is the same thickness. There is a link to the Royal Society paper jstor.org/stable/pdf/108649.pdf

– Yiannis Lazarides
2 hours ago





@DavidCarlisle No it is the same thickness. There is a link to the Royal Society paper jstor.org/stable/pdf/108649.pdf

– Yiannis Lazarides
2 hours ago










4 Answers
4






active

oldest

votes


















1














Here is an approximation, with basic commands:



documentclass{article}
usepackage{amsmath,amssymb,graphicx}

begin{document}

[ begin{array}{c@{}ccc@{}c}
(mkern 4.2mu{} & a &b & c &mkern 4.2mu)\[-0.31ex]
vline & a' &b' & c' & vline \
vline & a'' &b'' & c''& vline
end{array} ]%

end{document}


enter image description here






share|improve this answer































    1














    My proposal:



    documentclass{article}
    usepackage{amsmath,amssymb,graphicx}

    DeclareMathSymbol{A}{mathalpha}{operators}{`A}
    DeclareMathSymbol{B}{mathalpha}{operators}{`B}
    DeclareMathSymbol{C}{mathalpha}{operators}{`C}
    DeclareMathSymbol{D}{mathalpha}{operators}{`D}
    DeclareMathSymbol{E}{mathalpha}{operators}{`E}
    DeclareMathSymbol{F}{mathalpha}{operators}{`F}
    DeclareMathSymbol{G}{mathalpha}{operators}{`G}
    DeclareMathSymbol{H}{mathalpha}{operators}{`H}
    DeclareMathSymbol{I}{mathalpha}{operators}{`I}
    DeclareMathSymbol{J}{mathalpha}{operators}{`J}
    DeclareMathSymbol{K}{mathalpha}{operators}{`K}
    DeclareMathSymbol{L}{mathalpha}{operators}{`L}
    DeclareMathSymbol{M}{mathalpha}{operators}{`M}
    DeclareMathSymbol{N}{mathalpha}{operators}{`N}
    DeclareMathSymbol{O}{mathalpha}{operators}{`O}
    DeclareMathSymbol{P}{mathalpha}{operators}{`P}
    DeclareMathSymbol{Q}{mathalpha}{operators}{`Q}
    DeclareMathSymbol{R}{mathalpha}{operators}{`R}
    DeclareMathSymbol{S}{mathalpha}{operators}{`S}
    DeclareMathSymbol{T}{mathalpha}{operators}{`T}
    DeclareMathSymbol{U}{mathalpha}{operators}{`U}
    DeclareMathSymbol{V}{mathalpha}{operators}{`V}
    DeclareMathSymbol{W}{mathalpha}{operators}{`W}
    DeclareMathSymbol{X}{mathalpha}{operators}{`X}
    DeclareMathSymbol{Y}{mathalpha}{operators}{`Y}
    DeclareMathSymbol{Z}{mathalpha}{operators}{`Z}


    newsavebox{cayleybox}
    newlength{cayleyheight}
    newenvironment{cayleymatrix}[1]
    {begin{lrbox}{cayleybox}
    $begin{array}{@{enspace}l*{numexpr#1-1}{@{{,}enspace}l}@{enspace}}}
    {end{array}$end{lrbox}%
    setlength{cayleyheight}{dimexprhtcayleybox+dpcayleybox}%
    kern-0.8pt
    vtop to cayleyheight{hbox{vphantom{$between$}}leadersvrulevfill}%
    raisebox{dimexprhtstrutbox-htcayleybox}{useboxcayleybox}%
    vtop to cayleyheight{hbox{vphantom{$between$}}leadersvrulevfill}%
    kern-0.8pt
    }
    newcommand{by}{kern-0.4pt{between}kern-0.4pt}

    thinmuskip=6mu
    medmuskip=0mu
    thickmuskip=0mu

    begin{document}

    [ % page 17
    (X,Y,Z)=
    (begin{cayleymatrix}{3}
    a & b & c \
    a' & b' & c' \
    a'' & b'' & c''
    end{cayleymatrix}
    by x,y,z)
    ]

    [ % page 32
    (begin{cayleymatrix}{2} a & c \ b & d end{cayleymatrix} by
    begin{cayleymatrix}{2} a & b \ c & d end{cayleymatrix} by
    begin{cayleymatrix}{2} a & c \ b & d end{cayleymatrix} by
    begin{cayleymatrix}{2} a & b \ c & d end{cayleymatrix} )
    =
    bigl(
    (begin{cayleymatrix}{2} a & c \ b & d end{cayleymatrix}by
    begin{cayleymatrix}{2} a & b \ c & d end{cayleymatrix})
    bigr)^2
    ]

    end{document}


    enter image description here






    share|improve this answer































      1














      Extending Bernard's idea slightly:



      enter image description here



      ...but not quite up to the standards of egreg's nice solution:)



      documentclass{article}
      usepackage{array}
      newcounter{cayley}
      newcolumntype{L}{>{stepcounter{cayley}%
      ifnumvalue{cayley}=1raisebox{-0.4ex}{(}kern0.5exelsevlinefi}c@{}}
      newcolumntype{R}{@{}c<{spaceifnumvalue{cayley}=1kern0.5exraisebox{-0.4ex}{)}elsevlinefi}}
      newenvironment{cayley}[1][3]{setcounter{cayley}{0}array{L*{#1}{c}R}}{endarray}

      begin{document}

      [
      begin{cayley}
      &a & b & c &\
      &a' & b' & c' &\
      &a''& b''& c''&\
      end{cayley}
      qquad
      begin{cayley}[4]
      &a & b & c & d &\
      &a' & b' & c' & d' &\
      &a''& b''& c''& d''&\
      end{cayley}
      ]

      end{document}





      share|improve this answer































        0














        A TikZ proposal. Similarly to Andrew's nice answer you can focus on typing the matrix.



        documentclass{article}
        usepackage{tikz}
        makeatletter% https://tex.stackexchange.com/a/85531/121799
        longdefifnodedefined#1#2#3{%
        @ifundefined{pgf@sh@ns@#1}{#3}{#2}%
        }
        makeatother
        newcounter{CM}
        usetikzlibrary{matrix}
        newcommand{CayleyMatrix}[2][]{stepcounter{CM}%
        begin{tikzpicture}[baseline=(mat-numbervalue{CM}-1-1.base),inner sep=2pt,#1]
        matrix[matrix of math nodes,ampersand replacement=&] (mat-numbervalue{CM})
        { #2
        };
        ifnodedefined{mat-numbervalue{CM}-2-1}{%
        draw[semithick] (mat-numbervalue{CM}.south west) -- (mat-numbervalue{CM}.south west|-mat-numbervalue{CM}-1-1.south) to[out=135,in=-135]
        (mat-numbervalue{CM}.south west|-mat-numbervalue{CM}-1-1.north)
        (mat-numbervalue{CM}.south east) -- (mat-numbervalue{CM}.south east|-mat-numbervalue{CM}-1-1.south) to[out=45,in=-45]
        (mat-numbervalue{CM}.south east|-mat-numbervalue{CM}-1-1.north) ;}{
        draw[semithick] (mat-numbervalue{CM}.south west|-mat-numbervalue{CM}-1-1.south) to[out=135,in=-135]
        (mat-numbervalue{CM}.south west|-mat-numbervalue{CM}-1-1.north)
        (mat-numbervalue{CM}.south east|-mat-numbervalue{CM}-1-1.south) to[out=45,in=-45]
        (mat-numbervalue{CM}.south east|-mat-numbervalue{CM}-1-1.north) ;
        }
        end{tikzpicture}}
        begin{document}
        [CayleyMatrix{
        X &Y & Z \
        }=CayleyMatrix{
        a &b & c \
        a' &b' & c' \
        a'' & b'' & c'' \
        }!!CayleyMatrix{
        x &y & z \
        }]
        end{document}


        enter image description here






        share|improve this answer
























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          4 Answers
          4






          active

          oldest

          votes








          4 Answers
          4






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          1














          Here is an approximation, with basic commands:



          documentclass{article}
          usepackage{amsmath,amssymb,graphicx}

          begin{document}

          [ begin{array}{c@{}ccc@{}c}
          (mkern 4.2mu{} & a &b & c &mkern 4.2mu)\[-0.31ex]
          vline & a' &b' & c' & vline \
          vline & a'' &b'' & c''& vline
          end{array} ]%

          end{document}


          enter image description here






          share|improve this answer




























            1














            Here is an approximation, with basic commands:



            documentclass{article}
            usepackage{amsmath,amssymb,graphicx}

            begin{document}

            [ begin{array}{c@{}ccc@{}c}
            (mkern 4.2mu{} & a &b & c &mkern 4.2mu)\[-0.31ex]
            vline & a' &b' & c' & vline \
            vline & a'' &b'' & c''& vline
            end{array} ]%

            end{document}


            enter image description here






            share|improve this answer


























              1












              1








              1







              Here is an approximation, with basic commands:



              documentclass{article}
              usepackage{amsmath,amssymb,graphicx}

              begin{document}

              [ begin{array}{c@{}ccc@{}c}
              (mkern 4.2mu{} & a &b & c &mkern 4.2mu)\[-0.31ex]
              vline & a' &b' & c' & vline \
              vline & a'' &b'' & c''& vline
              end{array} ]%

              end{document}


              enter image description here






              share|improve this answer













              Here is an approximation, with basic commands:



              documentclass{article}
              usepackage{amsmath,amssymb,graphicx}

              begin{document}

              [ begin{array}{c@{}ccc@{}c}
              (mkern 4.2mu{} & a &b & c &mkern 4.2mu)\[-0.31ex]
              vline & a' &b' & c' & vline \
              vline & a'' &b'' & c''& vline
              end{array} ]%

              end{document}


              enter image description here







              share|improve this answer












              share|improve this answer



              share|improve this answer










              answered 1 hour ago









              BernardBernard

              177k779211




              177k779211























                  1














                  My proposal:



                  documentclass{article}
                  usepackage{amsmath,amssymb,graphicx}

                  DeclareMathSymbol{A}{mathalpha}{operators}{`A}
                  DeclareMathSymbol{B}{mathalpha}{operators}{`B}
                  DeclareMathSymbol{C}{mathalpha}{operators}{`C}
                  DeclareMathSymbol{D}{mathalpha}{operators}{`D}
                  DeclareMathSymbol{E}{mathalpha}{operators}{`E}
                  DeclareMathSymbol{F}{mathalpha}{operators}{`F}
                  DeclareMathSymbol{G}{mathalpha}{operators}{`G}
                  DeclareMathSymbol{H}{mathalpha}{operators}{`H}
                  DeclareMathSymbol{I}{mathalpha}{operators}{`I}
                  DeclareMathSymbol{J}{mathalpha}{operators}{`J}
                  DeclareMathSymbol{K}{mathalpha}{operators}{`K}
                  DeclareMathSymbol{L}{mathalpha}{operators}{`L}
                  DeclareMathSymbol{M}{mathalpha}{operators}{`M}
                  DeclareMathSymbol{N}{mathalpha}{operators}{`N}
                  DeclareMathSymbol{O}{mathalpha}{operators}{`O}
                  DeclareMathSymbol{P}{mathalpha}{operators}{`P}
                  DeclareMathSymbol{Q}{mathalpha}{operators}{`Q}
                  DeclareMathSymbol{R}{mathalpha}{operators}{`R}
                  DeclareMathSymbol{S}{mathalpha}{operators}{`S}
                  DeclareMathSymbol{T}{mathalpha}{operators}{`T}
                  DeclareMathSymbol{U}{mathalpha}{operators}{`U}
                  DeclareMathSymbol{V}{mathalpha}{operators}{`V}
                  DeclareMathSymbol{W}{mathalpha}{operators}{`W}
                  DeclareMathSymbol{X}{mathalpha}{operators}{`X}
                  DeclareMathSymbol{Y}{mathalpha}{operators}{`Y}
                  DeclareMathSymbol{Z}{mathalpha}{operators}{`Z}


                  newsavebox{cayleybox}
                  newlength{cayleyheight}
                  newenvironment{cayleymatrix}[1]
                  {begin{lrbox}{cayleybox}
                  $begin{array}{@{enspace}l*{numexpr#1-1}{@{{,}enspace}l}@{enspace}}}
                  {end{array}$end{lrbox}%
                  setlength{cayleyheight}{dimexprhtcayleybox+dpcayleybox}%
                  kern-0.8pt
                  vtop to cayleyheight{hbox{vphantom{$between$}}leadersvrulevfill}%
                  raisebox{dimexprhtstrutbox-htcayleybox}{useboxcayleybox}%
                  vtop to cayleyheight{hbox{vphantom{$between$}}leadersvrulevfill}%
                  kern-0.8pt
                  }
                  newcommand{by}{kern-0.4pt{between}kern-0.4pt}

                  thinmuskip=6mu
                  medmuskip=0mu
                  thickmuskip=0mu

                  begin{document}

                  [ % page 17
                  (X,Y,Z)=
                  (begin{cayleymatrix}{3}
                  a & b & c \
                  a' & b' & c' \
                  a'' & b'' & c''
                  end{cayleymatrix}
                  by x,y,z)
                  ]

                  [ % page 32
                  (begin{cayleymatrix}{2} a & c \ b & d end{cayleymatrix} by
                  begin{cayleymatrix}{2} a & b \ c & d end{cayleymatrix} by
                  begin{cayleymatrix}{2} a & c \ b & d end{cayleymatrix} by
                  begin{cayleymatrix}{2} a & b \ c & d end{cayleymatrix} )
                  =
                  bigl(
                  (begin{cayleymatrix}{2} a & c \ b & d end{cayleymatrix}by
                  begin{cayleymatrix}{2} a & b \ c & d end{cayleymatrix})
                  bigr)^2
                  ]

                  end{document}


                  enter image description here






                  share|improve this answer




























                    1














                    My proposal:



                    documentclass{article}
                    usepackage{amsmath,amssymb,graphicx}

                    DeclareMathSymbol{A}{mathalpha}{operators}{`A}
                    DeclareMathSymbol{B}{mathalpha}{operators}{`B}
                    DeclareMathSymbol{C}{mathalpha}{operators}{`C}
                    DeclareMathSymbol{D}{mathalpha}{operators}{`D}
                    DeclareMathSymbol{E}{mathalpha}{operators}{`E}
                    DeclareMathSymbol{F}{mathalpha}{operators}{`F}
                    DeclareMathSymbol{G}{mathalpha}{operators}{`G}
                    DeclareMathSymbol{H}{mathalpha}{operators}{`H}
                    DeclareMathSymbol{I}{mathalpha}{operators}{`I}
                    DeclareMathSymbol{J}{mathalpha}{operators}{`J}
                    DeclareMathSymbol{K}{mathalpha}{operators}{`K}
                    DeclareMathSymbol{L}{mathalpha}{operators}{`L}
                    DeclareMathSymbol{M}{mathalpha}{operators}{`M}
                    DeclareMathSymbol{N}{mathalpha}{operators}{`N}
                    DeclareMathSymbol{O}{mathalpha}{operators}{`O}
                    DeclareMathSymbol{P}{mathalpha}{operators}{`P}
                    DeclareMathSymbol{Q}{mathalpha}{operators}{`Q}
                    DeclareMathSymbol{R}{mathalpha}{operators}{`R}
                    DeclareMathSymbol{S}{mathalpha}{operators}{`S}
                    DeclareMathSymbol{T}{mathalpha}{operators}{`T}
                    DeclareMathSymbol{U}{mathalpha}{operators}{`U}
                    DeclareMathSymbol{V}{mathalpha}{operators}{`V}
                    DeclareMathSymbol{W}{mathalpha}{operators}{`W}
                    DeclareMathSymbol{X}{mathalpha}{operators}{`X}
                    DeclareMathSymbol{Y}{mathalpha}{operators}{`Y}
                    DeclareMathSymbol{Z}{mathalpha}{operators}{`Z}


                    newsavebox{cayleybox}
                    newlength{cayleyheight}
                    newenvironment{cayleymatrix}[1]
                    {begin{lrbox}{cayleybox}
                    $begin{array}{@{enspace}l*{numexpr#1-1}{@{{,}enspace}l}@{enspace}}}
                    {end{array}$end{lrbox}%
                    setlength{cayleyheight}{dimexprhtcayleybox+dpcayleybox}%
                    kern-0.8pt
                    vtop to cayleyheight{hbox{vphantom{$between$}}leadersvrulevfill}%
                    raisebox{dimexprhtstrutbox-htcayleybox}{useboxcayleybox}%
                    vtop to cayleyheight{hbox{vphantom{$between$}}leadersvrulevfill}%
                    kern-0.8pt
                    }
                    newcommand{by}{kern-0.4pt{between}kern-0.4pt}

                    thinmuskip=6mu
                    medmuskip=0mu
                    thickmuskip=0mu

                    begin{document}

                    [ % page 17
                    (X,Y,Z)=
                    (begin{cayleymatrix}{3}
                    a & b & c \
                    a' & b' & c' \
                    a'' & b'' & c''
                    end{cayleymatrix}
                    by x,y,z)
                    ]

                    [ % page 32
                    (begin{cayleymatrix}{2} a & c \ b & d end{cayleymatrix} by
                    begin{cayleymatrix}{2} a & b \ c & d end{cayleymatrix} by
                    begin{cayleymatrix}{2} a & c \ b & d end{cayleymatrix} by
                    begin{cayleymatrix}{2} a & b \ c & d end{cayleymatrix} )
                    =
                    bigl(
                    (begin{cayleymatrix}{2} a & c \ b & d end{cayleymatrix}by
                    begin{cayleymatrix}{2} a & b \ c & d end{cayleymatrix})
                    bigr)^2
                    ]

                    end{document}


                    enter image description here






                    share|improve this answer


























                      1












                      1








                      1







                      My proposal:



                      documentclass{article}
                      usepackage{amsmath,amssymb,graphicx}

                      DeclareMathSymbol{A}{mathalpha}{operators}{`A}
                      DeclareMathSymbol{B}{mathalpha}{operators}{`B}
                      DeclareMathSymbol{C}{mathalpha}{operators}{`C}
                      DeclareMathSymbol{D}{mathalpha}{operators}{`D}
                      DeclareMathSymbol{E}{mathalpha}{operators}{`E}
                      DeclareMathSymbol{F}{mathalpha}{operators}{`F}
                      DeclareMathSymbol{G}{mathalpha}{operators}{`G}
                      DeclareMathSymbol{H}{mathalpha}{operators}{`H}
                      DeclareMathSymbol{I}{mathalpha}{operators}{`I}
                      DeclareMathSymbol{J}{mathalpha}{operators}{`J}
                      DeclareMathSymbol{K}{mathalpha}{operators}{`K}
                      DeclareMathSymbol{L}{mathalpha}{operators}{`L}
                      DeclareMathSymbol{M}{mathalpha}{operators}{`M}
                      DeclareMathSymbol{N}{mathalpha}{operators}{`N}
                      DeclareMathSymbol{O}{mathalpha}{operators}{`O}
                      DeclareMathSymbol{P}{mathalpha}{operators}{`P}
                      DeclareMathSymbol{Q}{mathalpha}{operators}{`Q}
                      DeclareMathSymbol{R}{mathalpha}{operators}{`R}
                      DeclareMathSymbol{S}{mathalpha}{operators}{`S}
                      DeclareMathSymbol{T}{mathalpha}{operators}{`T}
                      DeclareMathSymbol{U}{mathalpha}{operators}{`U}
                      DeclareMathSymbol{V}{mathalpha}{operators}{`V}
                      DeclareMathSymbol{W}{mathalpha}{operators}{`W}
                      DeclareMathSymbol{X}{mathalpha}{operators}{`X}
                      DeclareMathSymbol{Y}{mathalpha}{operators}{`Y}
                      DeclareMathSymbol{Z}{mathalpha}{operators}{`Z}


                      newsavebox{cayleybox}
                      newlength{cayleyheight}
                      newenvironment{cayleymatrix}[1]
                      {begin{lrbox}{cayleybox}
                      $begin{array}{@{enspace}l*{numexpr#1-1}{@{{,}enspace}l}@{enspace}}}
                      {end{array}$end{lrbox}%
                      setlength{cayleyheight}{dimexprhtcayleybox+dpcayleybox}%
                      kern-0.8pt
                      vtop to cayleyheight{hbox{vphantom{$between$}}leadersvrulevfill}%
                      raisebox{dimexprhtstrutbox-htcayleybox}{useboxcayleybox}%
                      vtop to cayleyheight{hbox{vphantom{$between$}}leadersvrulevfill}%
                      kern-0.8pt
                      }
                      newcommand{by}{kern-0.4pt{between}kern-0.4pt}

                      thinmuskip=6mu
                      medmuskip=0mu
                      thickmuskip=0mu

                      begin{document}

                      [ % page 17
                      (X,Y,Z)=
                      (begin{cayleymatrix}{3}
                      a & b & c \
                      a' & b' & c' \
                      a'' & b'' & c''
                      end{cayleymatrix}
                      by x,y,z)
                      ]

                      [ % page 32
                      (begin{cayleymatrix}{2} a & c \ b & d end{cayleymatrix} by
                      begin{cayleymatrix}{2} a & b \ c & d end{cayleymatrix} by
                      begin{cayleymatrix}{2} a & c \ b & d end{cayleymatrix} by
                      begin{cayleymatrix}{2} a & b \ c & d end{cayleymatrix} )
                      =
                      bigl(
                      (begin{cayleymatrix}{2} a & c \ b & d end{cayleymatrix}by
                      begin{cayleymatrix}{2} a & b \ c & d end{cayleymatrix})
                      bigr)^2
                      ]

                      end{document}


                      enter image description here






                      share|improve this answer













                      My proposal:



                      documentclass{article}
                      usepackage{amsmath,amssymb,graphicx}

                      DeclareMathSymbol{A}{mathalpha}{operators}{`A}
                      DeclareMathSymbol{B}{mathalpha}{operators}{`B}
                      DeclareMathSymbol{C}{mathalpha}{operators}{`C}
                      DeclareMathSymbol{D}{mathalpha}{operators}{`D}
                      DeclareMathSymbol{E}{mathalpha}{operators}{`E}
                      DeclareMathSymbol{F}{mathalpha}{operators}{`F}
                      DeclareMathSymbol{G}{mathalpha}{operators}{`G}
                      DeclareMathSymbol{H}{mathalpha}{operators}{`H}
                      DeclareMathSymbol{I}{mathalpha}{operators}{`I}
                      DeclareMathSymbol{J}{mathalpha}{operators}{`J}
                      DeclareMathSymbol{K}{mathalpha}{operators}{`K}
                      DeclareMathSymbol{L}{mathalpha}{operators}{`L}
                      DeclareMathSymbol{M}{mathalpha}{operators}{`M}
                      DeclareMathSymbol{N}{mathalpha}{operators}{`N}
                      DeclareMathSymbol{O}{mathalpha}{operators}{`O}
                      DeclareMathSymbol{P}{mathalpha}{operators}{`P}
                      DeclareMathSymbol{Q}{mathalpha}{operators}{`Q}
                      DeclareMathSymbol{R}{mathalpha}{operators}{`R}
                      DeclareMathSymbol{S}{mathalpha}{operators}{`S}
                      DeclareMathSymbol{T}{mathalpha}{operators}{`T}
                      DeclareMathSymbol{U}{mathalpha}{operators}{`U}
                      DeclareMathSymbol{V}{mathalpha}{operators}{`V}
                      DeclareMathSymbol{W}{mathalpha}{operators}{`W}
                      DeclareMathSymbol{X}{mathalpha}{operators}{`X}
                      DeclareMathSymbol{Y}{mathalpha}{operators}{`Y}
                      DeclareMathSymbol{Z}{mathalpha}{operators}{`Z}


                      newsavebox{cayleybox}
                      newlength{cayleyheight}
                      newenvironment{cayleymatrix}[1]
                      {begin{lrbox}{cayleybox}
                      $begin{array}{@{enspace}l*{numexpr#1-1}{@{{,}enspace}l}@{enspace}}}
                      {end{array}$end{lrbox}%
                      setlength{cayleyheight}{dimexprhtcayleybox+dpcayleybox}%
                      kern-0.8pt
                      vtop to cayleyheight{hbox{vphantom{$between$}}leadersvrulevfill}%
                      raisebox{dimexprhtstrutbox-htcayleybox}{useboxcayleybox}%
                      vtop to cayleyheight{hbox{vphantom{$between$}}leadersvrulevfill}%
                      kern-0.8pt
                      }
                      newcommand{by}{kern-0.4pt{between}kern-0.4pt}

                      thinmuskip=6mu
                      medmuskip=0mu
                      thickmuskip=0mu

                      begin{document}

                      [ % page 17
                      (X,Y,Z)=
                      (begin{cayleymatrix}{3}
                      a & b & c \
                      a' & b' & c' \
                      a'' & b'' & c''
                      end{cayleymatrix}
                      by x,y,z)
                      ]

                      [ % page 32
                      (begin{cayleymatrix}{2} a & c \ b & d end{cayleymatrix} by
                      begin{cayleymatrix}{2} a & b \ c & d end{cayleymatrix} by
                      begin{cayleymatrix}{2} a & c \ b & d end{cayleymatrix} by
                      begin{cayleymatrix}{2} a & b \ c & d end{cayleymatrix} )
                      =
                      bigl(
                      (begin{cayleymatrix}{2} a & c \ b & d end{cayleymatrix}by
                      begin{cayleymatrix}{2} a & b \ c & d end{cayleymatrix})
                      bigr)^2
                      ]

                      end{document}


                      enter image description here







                      share|improve this answer












                      share|improve this answer



                      share|improve this answer










                      answered 49 mins ago









                      egregegreg

                      737k8919363264




                      737k8919363264























                          1














                          Extending Bernard's idea slightly:



                          enter image description here



                          ...but not quite up to the standards of egreg's nice solution:)



                          documentclass{article}
                          usepackage{array}
                          newcounter{cayley}
                          newcolumntype{L}{>{stepcounter{cayley}%
                          ifnumvalue{cayley}=1raisebox{-0.4ex}{(}kern0.5exelsevlinefi}c@{}}
                          newcolumntype{R}{@{}c<{spaceifnumvalue{cayley}=1kern0.5exraisebox{-0.4ex}{)}elsevlinefi}}
                          newenvironment{cayley}[1][3]{setcounter{cayley}{0}array{L*{#1}{c}R}}{endarray}

                          begin{document}

                          [
                          begin{cayley}
                          &a & b & c &\
                          &a' & b' & c' &\
                          &a''& b''& c''&\
                          end{cayley}
                          qquad
                          begin{cayley}[4]
                          &a & b & c & d &\
                          &a' & b' & c' & d' &\
                          &a''& b''& c''& d''&\
                          end{cayley}
                          ]

                          end{document}





                          share|improve this answer




























                            1














                            Extending Bernard's idea slightly:



                            enter image description here



                            ...but not quite up to the standards of egreg's nice solution:)



                            documentclass{article}
                            usepackage{array}
                            newcounter{cayley}
                            newcolumntype{L}{>{stepcounter{cayley}%
                            ifnumvalue{cayley}=1raisebox{-0.4ex}{(}kern0.5exelsevlinefi}c@{}}
                            newcolumntype{R}{@{}c<{spaceifnumvalue{cayley}=1kern0.5exraisebox{-0.4ex}{)}elsevlinefi}}
                            newenvironment{cayley}[1][3]{setcounter{cayley}{0}array{L*{#1}{c}R}}{endarray}

                            begin{document}

                            [
                            begin{cayley}
                            &a & b & c &\
                            &a' & b' & c' &\
                            &a''& b''& c''&\
                            end{cayley}
                            qquad
                            begin{cayley}[4]
                            &a & b & c & d &\
                            &a' & b' & c' & d' &\
                            &a''& b''& c''& d''&\
                            end{cayley}
                            ]

                            end{document}





                            share|improve this answer


























                              1












                              1








                              1







                              Extending Bernard's idea slightly:



                              enter image description here



                              ...but not quite up to the standards of egreg's nice solution:)



                              documentclass{article}
                              usepackage{array}
                              newcounter{cayley}
                              newcolumntype{L}{>{stepcounter{cayley}%
                              ifnumvalue{cayley}=1raisebox{-0.4ex}{(}kern0.5exelsevlinefi}c@{}}
                              newcolumntype{R}{@{}c<{spaceifnumvalue{cayley}=1kern0.5exraisebox{-0.4ex}{)}elsevlinefi}}
                              newenvironment{cayley}[1][3]{setcounter{cayley}{0}array{L*{#1}{c}R}}{endarray}

                              begin{document}

                              [
                              begin{cayley}
                              &a & b & c &\
                              &a' & b' & c' &\
                              &a''& b''& c''&\
                              end{cayley}
                              qquad
                              begin{cayley}[4]
                              &a & b & c & d &\
                              &a' & b' & c' & d' &\
                              &a''& b''& c''& d''&\
                              end{cayley}
                              ]

                              end{document}





                              share|improve this answer













                              Extending Bernard's idea slightly:



                              enter image description here



                              ...but not quite up to the standards of egreg's nice solution:)



                              documentclass{article}
                              usepackage{array}
                              newcounter{cayley}
                              newcolumntype{L}{>{stepcounter{cayley}%
                              ifnumvalue{cayley}=1raisebox{-0.4ex}{(}kern0.5exelsevlinefi}c@{}}
                              newcolumntype{R}{@{}c<{spaceifnumvalue{cayley}=1kern0.5exraisebox{-0.4ex}{)}elsevlinefi}}
                              newenvironment{cayley}[1][3]{setcounter{cayley}{0}array{L*{#1}{c}R}}{endarray}

                              begin{document}

                              [
                              begin{cayley}
                              &a & b & c &\
                              &a' & b' & c' &\
                              &a''& b''& c''&\
                              end{cayley}
                              qquad
                              begin{cayley}[4]
                              &a & b & c & d &\
                              &a' & b' & c' & d' &\
                              &a''& b''& c''& d''&\
                              end{cayley}
                              ]

                              end{document}






                              share|improve this answer












                              share|improve this answer



                              share|improve this answer










                              answered 22 mins ago









                              AndrewAndrew

                              31.4k34483




                              31.4k34483























                                  0














                                  A TikZ proposal. Similarly to Andrew's nice answer you can focus on typing the matrix.



                                  documentclass{article}
                                  usepackage{tikz}
                                  makeatletter% https://tex.stackexchange.com/a/85531/121799
                                  longdefifnodedefined#1#2#3{%
                                  @ifundefined{pgf@sh@ns@#1}{#3}{#2}%
                                  }
                                  makeatother
                                  newcounter{CM}
                                  usetikzlibrary{matrix}
                                  newcommand{CayleyMatrix}[2][]{stepcounter{CM}%
                                  begin{tikzpicture}[baseline=(mat-numbervalue{CM}-1-1.base),inner sep=2pt,#1]
                                  matrix[matrix of math nodes,ampersand replacement=&] (mat-numbervalue{CM})
                                  { #2
                                  };
                                  ifnodedefined{mat-numbervalue{CM}-2-1}{%
                                  draw[semithick] (mat-numbervalue{CM}.south west) -- (mat-numbervalue{CM}.south west|-mat-numbervalue{CM}-1-1.south) to[out=135,in=-135]
                                  (mat-numbervalue{CM}.south west|-mat-numbervalue{CM}-1-1.north)
                                  (mat-numbervalue{CM}.south east) -- (mat-numbervalue{CM}.south east|-mat-numbervalue{CM}-1-1.south) to[out=45,in=-45]
                                  (mat-numbervalue{CM}.south east|-mat-numbervalue{CM}-1-1.north) ;}{
                                  draw[semithick] (mat-numbervalue{CM}.south west|-mat-numbervalue{CM}-1-1.south) to[out=135,in=-135]
                                  (mat-numbervalue{CM}.south west|-mat-numbervalue{CM}-1-1.north)
                                  (mat-numbervalue{CM}.south east|-mat-numbervalue{CM}-1-1.south) to[out=45,in=-45]
                                  (mat-numbervalue{CM}.south east|-mat-numbervalue{CM}-1-1.north) ;
                                  }
                                  end{tikzpicture}}
                                  begin{document}
                                  [CayleyMatrix{
                                  X &Y & Z \
                                  }=CayleyMatrix{
                                  a &b & c \
                                  a' &b' & c' \
                                  a'' & b'' & c'' \
                                  }!!CayleyMatrix{
                                  x &y & z \
                                  }]
                                  end{document}


                                  enter image description here






                                  share|improve this answer




























                                    0














                                    A TikZ proposal. Similarly to Andrew's nice answer you can focus on typing the matrix.



                                    documentclass{article}
                                    usepackage{tikz}
                                    makeatletter% https://tex.stackexchange.com/a/85531/121799
                                    longdefifnodedefined#1#2#3{%
                                    @ifundefined{pgf@sh@ns@#1}{#3}{#2}%
                                    }
                                    makeatother
                                    newcounter{CM}
                                    usetikzlibrary{matrix}
                                    newcommand{CayleyMatrix}[2][]{stepcounter{CM}%
                                    begin{tikzpicture}[baseline=(mat-numbervalue{CM}-1-1.base),inner sep=2pt,#1]
                                    matrix[matrix of math nodes,ampersand replacement=&] (mat-numbervalue{CM})
                                    { #2
                                    };
                                    ifnodedefined{mat-numbervalue{CM}-2-1}{%
                                    draw[semithick] (mat-numbervalue{CM}.south west) -- (mat-numbervalue{CM}.south west|-mat-numbervalue{CM}-1-1.south) to[out=135,in=-135]
                                    (mat-numbervalue{CM}.south west|-mat-numbervalue{CM}-1-1.north)
                                    (mat-numbervalue{CM}.south east) -- (mat-numbervalue{CM}.south east|-mat-numbervalue{CM}-1-1.south) to[out=45,in=-45]
                                    (mat-numbervalue{CM}.south east|-mat-numbervalue{CM}-1-1.north) ;}{
                                    draw[semithick] (mat-numbervalue{CM}.south west|-mat-numbervalue{CM}-1-1.south) to[out=135,in=-135]
                                    (mat-numbervalue{CM}.south west|-mat-numbervalue{CM}-1-1.north)
                                    (mat-numbervalue{CM}.south east|-mat-numbervalue{CM}-1-1.south) to[out=45,in=-45]
                                    (mat-numbervalue{CM}.south east|-mat-numbervalue{CM}-1-1.north) ;
                                    }
                                    end{tikzpicture}}
                                    begin{document}
                                    [CayleyMatrix{
                                    X &Y & Z \
                                    }=CayleyMatrix{
                                    a &b & c \
                                    a' &b' & c' \
                                    a'' & b'' & c'' \
                                    }!!CayleyMatrix{
                                    x &y & z \
                                    }]
                                    end{document}


                                    enter image description here






                                    share|improve this answer


























                                      0












                                      0








                                      0







                                      A TikZ proposal. Similarly to Andrew's nice answer you can focus on typing the matrix.



                                      documentclass{article}
                                      usepackage{tikz}
                                      makeatletter% https://tex.stackexchange.com/a/85531/121799
                                      longdefifnodedefined#1#2#3{%
                                      @ifundefined{pgf@sh@ns@#1}{#3}{#2}%
                                      }
                                      makeatother
                                      newcounter{CM}
                                      usetikzlibrary{matrix}
                                      newcommand{CayleyMatrix}[2][]{stepcounter{CM}%
                                      begin{tikzpicture}[baseline=(mat-numbervalue{CM}-1-1.base),inner sep=2pt,#1]
                                      matrix[matrix of math nodes,ampersand replacement=&] (mat-numbervalue{CM})
                                      { #2
                                      };
                                      ifnodedefined{mat-numbervalue{CM}-2-1}{%
                                      draw[semithick] (mat-numbervalue{CM}.south west) -- (mat-numbervalue{CM}.south west|-mat-numbervalue{CM}-1-1.south) to[out=135,in=-135]
                                      (mat-numbervalue{CM}.south west|-mat-numbervalue{CM}-1-1.north)
                                      (mat-numbervalue{CM}.south east) -- (mat-numbervalue{CM}.south east|-mat-numbervalue{CM}-1-1.south) to[out=45,in=-45]
                                      (mat-numbervalue{CM}.south east|-mat-numbervalue{CM}-1-1.north) ;}{
                                      draw[semithick] (mat-numbervalue{CM}.south west|-mat-numbervalue{CM}-1-1.south) to[out=135,in=-135]
                                      (mat-numbervalue{CM}.south west|-mat-numbervalue{CM}-1-1.north)
                                      (mat-numbervalue{CM}.south east|-mat-numbervalue{CM}-1-1.south) to[out=45,in=-45]
                                      (mat-numbervalue{CM}.south east|-mat-numbervalue{CM}-1-1.north) ;
                                      }
                                      end{tikzpicture}}
                                      begin{document}
                                      [CayleyMatrix{
                                      X &Y & Z \
                                      }=CayleyMatrix{
                                      a &b & c \
                                      a' &b' & c' \
                                      a'' & b'' & c'' \
                                      }!!CayleyMatrix{
                                      x &y & z \
                                      }]
                                      end{document}


                                      enter image description here






                                      share|improve this answer













                                      A TikZ proposal. Similarly to Andrew's nice answer you can focus on typing the matrix.



                                      documentclass{article}
                                      usepackage{tikz}
                                      makeatletter% https://tex.stackexchange.com/a/85531/121799
                                      longdefifnodedefined#1#2#3{%
                                      @ifundefined{pgf@sh@ns@#1}{#3}{#2}%
                                      }
                                      makeatother
                                      newcounter{CM}
                                      usetikzlibrary{matrix}
                                      newcommand{CayleyMatrix}[2][]{stepcounter{CM}%
                                      begin{tikzpicture}[baseline=(mat-numbervalue{CM}-1-1.base),inner sep=2pt,#1]
                                      matrix[matrix of math nodes,ampersand replacement=&] (mat-numbervalue{CM})
                                      { #2
                                      };
                                      ifnodedefined{mat-numbervalue{CM}-2-1}{%
                                      draw[semithick] (mat-numbervalue{CM}.south west) -- (mat-numbervalue{CM}.south west|-mat-numbervalue{CM}-1-1.south) to[out=135,in=-135]
                                      (mat-numbervalue{CM}.south west|-mat-numbervalue{CM}-1-1.north)
                                      (mat-numbervalue{CM}.south east) -- (mat-numbervalue{CM}.south east|-mat-numbervalue{CM}-1-1.south) to[out=45,in=-45]
                                      (mat-numbervalue{CM}.south east|-mat-numbervalue{CM}-1-1.north) ;}{
                                      draw[semithick] (mat-numbervalue{CM}.south west|-mat-numbervalue{CM}-1-1.south) to[out=135,in=-135]
                                      (mat-numbervalue{CM}.south west|-mat-numbervalue{CM}-1-1.north)
                                      (mat-numbervalue{CM}.south east|-mat-numbervalue{CM}-1-1.south) to[out=45,in=-45]
                                      (mat-numbervalue{CM}.south east|-mat-numbervalue{CM}-1-1.north) ;
                                      }
                                      end{tikzpicture}}
                                      begin{document}
                                      [CayleyMatrix{
                                      X &Y & Z \
                                      }=CayleyMatrix{
                                      a &b & c \
                                      a' &b' & c' \
                                      a'' & b'' & c'' \
                                      }!!CayleyMatrix{
                                      x &y & z \
                                      }]
                                      end{document}


                                      enter image description here







                                      share|improve this answer












                                      share|improve this answer



                                      share|improve this answer










                                      answered 11 mins ago









                                      marmotmarmot

                                      121k6158296




                                      121k6158296






























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