Csdrhrt

I need to create a determinant (vmatrix) as shown in this picture. So, I wrote a simple LaTEX file for testing purposes as follows:

documentclass[a4paper,10pt]{article}



usepackage{amsmath}



begin{document}



begin{equation*}

        begin{vmatrix}

                0     &cdot &cdot &0     &a_{1} alpha_{1}+ cdots +k_{1} alpha_{n} &cdot &cdot &a_{1} kappa_{1}+ cdots +k_{1} kappa_{n} \

                cdot &cdot &cdot &cdot &cdot                                      &cdot &cdot &cdot \

                0     &cdot &cdot &0     &a_{n} alpha_{1}+ cdots +k_{n} alpha_{n} &cdot &cdot &a_{n} kappa_{1}+ cdots +k_{n} kappa_{n} \

                -1    &cdot &cdot &0     &alpha_{1}                                 &cdot &cdot &kappa_{1} \

                cdot &cdot &cdot &cdot &cdot                                      &cdot &cdot &cdot \

                0     &cdot &cdot &-1    &alpha_{n}                                 &cdot &cdot &kappa_{n}

        end{vmatrix}

end{equation*}



end{document}

When the above file gets compiled with TeXLive on a Linux desktop computer, it produces the following ugly result: I thought using hdotsfor{} for the horizontal line, but the spacing between the dots is too close. If there is a simple way to tell hdotsfor{} to skip every dot, I believe that would do. However, perhaps someone here knows a much better way.

This seems a good approximation:

documentclass[a4paper,10pt]{article}



usepackage{amsmath}



newcommand{widedots}{%

  .cleadershbox to 2tabcolsep{hss.hss}hfill.%

  hspace*{0pt}%

}



begin{document}



begin{equation*}

newcommand{ak}[2]{%

  makebox[14tabcolsep][s]{$displaystyle a_{#2}#1_1+dots+k_{#2}#1_n$}%

}

begin{vmatrix}

 0 & . & . &  0 & ak{alpha}{1} & . & . & ak{kappa}{1} \

 . & . & . &  . & widedots      & . & . & widedots      \

 0 & . & . &  0 & ak{alpha}{n} & . & . & ak{kappa}{n} \

-1 & . & . &  0 & alpha_{1}     & . & . & kappa_{1}     \

 . & . & . &  . & widedots      & . & . & widedots      \

 0 & . & . & -1 & alpha_{n}     & . & . & kappa_{n}

end{vmatrix}

end{equation*}



end{document}

The value 14tabcolsep has been determined by first looking at the entries at their natural width.

Even better than the original if we make -1 to hide its width.

documentclass[a4paper,10pt]{article}



usepackage{amsmath}



newcommand{widedots}{%

  .cleadershbox to 2tabcolsep{hss.hss}hfill.%

  hspace*{0pt}%

}



begin{document}



begin{equation*}

newcommand{ak}[2]{%

  makebox[14tabcolsep][s]{$displaystyle a_{#2}#1_1+dots+k_{#2}#1_n$}%

}

newcommand{?}{makebox[0pt]{$-1$}}

begin{vmatrix}mspace{8mu}

begin{matrix}

 0 & . & . &  0 & ak{alpha}{1} & . & . & ak{kappa}{1} \

 . & . & . &  . & widedots      & . & . & widedots      \

 0 & . & . &  0 & ak{alpha}{n} & . & . & ak{kappa}{n} \

? & . & . &  0 & alpha_{1}     & . & . & kappa_{1}     \

 . & . & . &  . & widedots      & . & . & widedots      \

 0 & . & . & ? & alpha_{n}     & . & . & kappa_{n}

end{matrix}mspace{3mu}

end{vmatrix}

end{equation*}



end{document}

With dots and hdotsfor:

begin{equation*}

newcommand{ak}[2]{a_{#2}#1_1+dots+k_{#2}#1_n}

begin{vmatrix}

 0 & dots &  0 & ak{alpha}{1} & dots & ak{kappa}{1} \

hdotsfor{6} \

 0 & dots &  0 & ak{alpha}{n} & dots & ak{kappa}{n} \

-1 & dots &  0 & alpha_{1}     & dots & kappa_{1}     \

hdotsfor{6} \

 0 & dots & -1 & alpha_{n}     & dots & kappa_{n}

end{vmatrix}

end{equation*}

One way is to manually put dots with some horizontal space.

documentclass[a4paper,10pt]{article}

usepackage{amsmath}

begin{document}



begin{equation*}

        begin{vmatrix}

                0     &cdot &cdot &0     &a_{1} alpha_{1}+ cdots +k_{1} alpha_{n} &cdot &cdot &a_{1} kappa_{1}+ cdots +k_{1} kappa_{n} \

                cdot &cdot &cdot &cdot &cdot hfil hfil cdot hfil cdot hfil cdot hfil cdot                               &cdot &cdot &cdot hfil hfil cdot hfil cdot hfil cdot hfil cdot  \

                0     &cdot &cdot &0     &a_{n} alpha_{1}+ cdots +k_{n} alpha_{n} &cdot &cdot &a_{n} kappa_{1}+ cdots +k_{n} kappa_{n} \

                -1    &cdot &cdot &0     &alpha_{1}                                 &cdot &cdot &kappa_{1} \

                cdot &cdot &cdot &cdot &cdot hfil hfil cdot hfil cdot hfil cdot hfil cdot                                      &cdot &cdot &cdot hfil hfil cdot hfil cdot hfil cdot hfil cdot  \

                0     &cdot &cdot &-1    &alpha_{n}                                 &cdot &cdot &kappa_{n}

        end{vmatrix}

end{equation*}



end{document}

Defining two newcommands twodts and fivedts for empty columns and rows can simplify the table.

documentclass[a4paper,10pt]{article}

usepackage{amsmath}



begin{document}



newcommand{twodts}{begin{tabular}{@{}cc@{}}$cdot$&$cdot$end{tabular}}

newcommand{fivedts}{begin{tabular}{@{}*5{c}@{}}$cdot$&$cdot$&$cdot$&$cdot$&$cdot$end{tabular}}



begin{equation*}

  begin{array}{|cccccc|}

    0     & twodts & 0     & a_1 alpha_1+ cdots +k_1 alpha_n & twodts & a_1 kappa_1+ cdots +k_1 kappa_n \

    cdot & twodts & cdot & fivedts                           & twodts & fivedts                           \

    0     & twodts & 0     & a_n alpha_1+ cdots +k_n alpha_n & twodts & a_n kappa_1+ cdots +k_n kappa_n \

    -1    & twodts & 0     & alpha_1                           & twodts & kappa_1                           \

    cdot & twodts & cdot & fivedts                           & twodts & fivedts                           \

    0     & twodts & -1    & alpha_n                           & twodts & kappa_n

  end{array}

end{equation*}



end{document}

Update:

You can easily adapt my answer to add six dots instead of five like this:

documentclass[a4paper,10pt]{article}

usepackage{amsmath,array}



begin{document}



deftwocdots{$cdot$&$cdot$}

newcommand{twodts}{begin{tabular}{@{}cc@{}}twocdotsend{tabular}}

newcommand{sixdts}{begin{tabular}{@{}*6{c}@{}}twocdots&twocdots&twocdotsend{tabular}}



begin{equation*}

  begin{array}{|cccccc|}

    0     & twodts & 0     & a_1 alpha_1+ cdots +k_1 alpha_n & twodts & a_1 kappa_1+ cdots +k_1 kappa_n \

    cdot & twodts & cdot & sixdts                            & twodts & sixdts                            \

    0     & twodts & 0     & a_n alpha_1+ cdots +k_n alpha_n & twodts & a_n kappa_1+ cdots +k_n kappa_n \

    -1    & twodts & 0     & alpha_1                           & twodts & kappa_1                           \

    cdot & twodts & cdot & sixdts                            & twodts & sixdts                            \

    0     & twodts & -1    & alpha_n                           & twodts & kappa_n

  end{array}

end{equation*}



end{document}

Would this be acceptable?

documentclass[a4paper,10pt]{article}



usepackage{amsmath}



begin{document}



begin{equation*}

           begin{vmatrix}

            0     &cdots &0     &a_{1} alpha_{1}+ cdots +k_{1} alpha_{n} &cdots     &a_{1} kappa_{1}+ cdots +k_{1} kappa_{n} \

            vdots &ddots &vdots &vdots &ddots  &vdots \

            0     &cdots & 0     &a_{n} alpha_{1}+ cdots +k_{n} alpha_{n} &cdots  &a_{n} kappa_{1}+ cdots +k_{n} kappa_{n} \

            -1    &cdots &0     &alpha_{1}  &cdots &kappa_{1} \

            vdots &ddots &vdots &vdots   &ddots &vdots \

            0     &cdots & -1    &alpha_{n}  &cdots &kappa_{n}

    end{vmatrix}

end{equation*}



end{document}