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I want to draw the following matrix in LaTeX:

I found that I should use the TikZ package, and I have spent a lot of time looking at the package. However, I have no experience of using the package before, and I do not know how to draw it. How can I do it?

Just arrays:

documentclass{article}

usepackage{amsmath,array}



begin{document}



[

newcommand{blocke}{

  begin{matrix}

  hphantom{0} & hphantom{0} & hphantom{0} & hphantom{0} \

  \ \

  end{matrix}

}

newcommand{blockr}{

  begin{matrix}

  hphantom{0} & hphantom{0} & hphantom{0} &

  hat{N}smash[b]{vphantom{Big|}} \ &&& vdots \ &&& 2 \ &&& 1

  end{matrix}

}

newcommand{blockl}{

  begin{matrix}

  1 & hphantom{0} & hphantom{0} & hphantom{0} \

  2 \ vdots \ hat{N}smash[b]{vphantom{Big|}}

  end{matrix}

}

newcommand{dddots}{

  begin{matrix}

  hphantom{0} & hphantom{0} & ddots \

  \

  \

  ddots

  end{matrix}

}

begin{pmatrix}

hspace*{0.3em}

begin{array}{|*{5}{@{,}c@{!}|}}

hline

& blockl & & & blocke \

hline

blockr & & blockl & & \

hline

& blockr & & blockl & \

hline

& & & dddots & \

hline

& & & blockr & \

hline

end{array}

hspace*{0.3em}

end{pmatrix}

]



end{document}

I locally defined a few commands to ease input.

Welcome to TeX.SE! Actually, you do not need TikZ for this.

documentclass{article}

usepackage{amsmath}

begin{document}

[left(begin{array}{|*{5}{ccccc|}}

hline

& & & & & 1 & & & & & & & & & & & & & & & & & & &  \

& & & & & 2 & & & & & & & & & & & & & & & & & & &  \

& & & & & vdots & & & & & & & & & & & & & & & & & & &  \

& & & & & vdots & & & & & & & & & & & & & & & & & & &  \

& & & & & widehat{N} & & & & & & & & & & & & & & & & & & &  \

hline

& & & & widehat{N} & & & & & & 1 & & & & & & & & & & & & & &  \

& & & & vdots & & & & & & 2 & & & & & & & & & & & & & &  \

& & & & vdots & & & & & & vdots & & & & & & & & & & & & & &  \

& & & & 2 & & & & & & vdots & & & & & & & & & & & & & &  \

& & & & 1 & & & & & & widehat{N} & & & & & & & & & & & & & &  \

hline

& & & & & & & & & widehat{N} & & & & & & 1 & & & & & & & & &   \

& & & & & & & & & vdots & & & & & & 2 & & & & & & & & &    \

& & & & & & & & & vdots & & & & & & vdots & & & & & & & & &   \

& & & & & & & & & 2 & & & & & & vdots & & & & & & & & &   \

& & & & & & & & & 1 & & & & & & widehat{N} & & & & & & & & &   \

hline

& & & & & & & & & & & & & & & & & bullet & & & & & & &  \

& & & & & & & & & & & & & & & & & & bullet & & & & & &  \

& & & & & & & & & & & & & & & bullet & & & & bullet & & & & &  \

& & & & & & & & & & & & & & & & bullet & & & & & & & &  \

& & & & & & & & & & & & & & & & & bullet & & & & & & &  \

hline

& & & & & & & & & & & & & & & & & & & widehat{N} & & & & &  \

& & & & & & & & & & & & & & & & & & & vdots & & & & &  \

& & & & & & & & & & & & & & & & & & & vdots & & & & &  \

& & & & & & & & & & & & & & & & & & & 2 & & & & &  \

& & & & & & & & & & & & & & & & & & & 1 & & & & &  \

hline

end{array}right)]

end{document}

However, you could use TikZ to improve the appearance.

documentclass{article}

usepackage{amsmath}

usepackage{tikz}

usetikzlibrary{tikzmark}

tikzset{% https://tex.stackexchange.com/a/156990/121799

  dots/.style args={#1per #2}{%

    line cap=round,

    dash pattern=on 0 off #2/#1

  }

}

begin{document}

[left(begin{array}{|*{5}{ccccc|}}

hline

& & & & & 1 & & & & & & & & & & & & & & & & & & &  \

& & & & & tikzmarknode{21}{2} & & & & & & & & & & & & & & & & & & &  \

& & & & &  & & & & & & & & & & & & & & & & & & &  \

& & & & &  & & & & & & & & & & & & & & & & & & &  \

& & & & & tikzmarknode{N1}{widehat{N}} & & & & & & & & & & & & & & & & & & &  \

hline

& & & & tikzmarknode{N2}{widehat{N}} & & & & & & 1 & & & & & & & & & & & & & &  \

& & & & & & & & & & tikzmarknode{23}{2} & & & & & & & & & & & & & &  \

& & & &  & & & & & &  & & & & & & & & & & & & & &  \

& & & & tikzmarknode{22}{2} & & & & & &  & & & & & & & & & & & & & &  \

& & & & 1 & & & & & & tikzmarknode{N3}{widehat{N}} & & & & & & & & & & & & & &  \

hline

& & & & & & & & & tikzmarknode{N4}{widehat{N}} & & & & & & 1 & & & & & & & & &   \

& & & & & & & & &  & & & & & & tikzmarknode{25}{2} & & & & & & & & &    \

& & & & & & & & &  & & & & & &  & & & & & & & & &   \

& & & & & & & & & tikzmarknode{24}{2} & & & & & &  & & & & & & & & &   \

& & & & & & & & & 1 & & & & & & tikzmarknode{N5}{widehat{N}} & & & & & & & & &   \

hline

& & & & & & & & & & & & & & & & & bullet & & & & & & &  \

& & & & & & & & & & & & & & & & & & bullet & & & & & &  \

& & & & & & & & & & & & & & & bullet & & & & bullet & & & & &  \

& & & & & & & & & & & & & & & & bullet & & & & & & & &  \

& & & & & & & & & & & & & & & & & bullet & & & & & & &  \

hline

& & & & & & & & & & & & & & & & & & & tikzmarknode{N6}{widehat{N}} & & & & &  \

& & & & & & & & & & & & & & & & & & &  & & & & &  \

& & & & & & & & & & & & & & & & & & &  & & & & &  \

& & & & & & & & & & & & & & & & & & & tikzmarknode{26}{2} & & & & &  \

& & & & & & & & & & & & & & & & & & & 1 & & & & &  \

hline

end{array}right)]

begin{tikzpicture}[overlay,remember picture]

foreach X in {1,...,6}

{draw[very thick, dots=8 per 1cm,shorten >=3pt,shorten <=3pt] (2X) -- (NX);}

end{tikzpicture}

end{document}

ADDENDUM: In an attempt to make Ryan Reich a bit happy, here is a version in which you only have to specify the nonempty entries of this sparse array. These entries are determined by the list {6/1/1,6/2/2,6/5/widehat{N},... }, where each entry has the structure <X>/<Y>/<entry> with X and Y specifying the position. Notice that one could shorten this further if you really have only one type of columns, but the point here is to allow to build arbitrary sparse matrices of that type. This code uses this answer.

documentclass{article}

usepackage{tikz}

usetikzlibrary{matrix,calc}

usepackage{etoolbox}

tikzset{% https://tex.stackexchange.com/a/156990/121799

  dots/.style args={#1per #2}{%

    line cap=round,

    dash pattern=on 0 off #2/#1

  }

}

begin{document}

edefmylist{6/1/1,6/2/2,6/5/widehat{N},%

5/6/widehat{N},5/9/2,5/10/1,%

11/6/1,11/7/2,11/10/widehat{N},%

10/11/widehat{N},10/12/2,10/15/1,%

16/11/1,16/12/2,16/15/widehat{N},%

20/21/widehat{N},20/22/2,20/25/1%

}

begin{tikzpicture}

    letmymatrixcontentempty

    foreach Y in {1,...,25}{%

        foreach X in {1,...,25}

        {xdeftmp{{}}

         foreach XX/YY/ZZ in mylist

          {ifnumXX=X

           ifnumYY=Y

            xdeftmp{ZZ}

           fi

          fi}

          ifnumX=25

             expandaftergapptoexpandaftermymatrixcontentexpandafter{tmpspace\}% 

          else

            expandaftergapptoexpandaftermymatrixcontentexpandafter{tmpspace&space}%

          fi   

        }

    }

    matrix [matrix of math nodes,ampersand replacement=&,left delimiter=(,

    right delimiter=),draw,row sep=3pt] (mat) {

        mymatrixcontent

    };

    foreach X [evaluate=X as Y using {int(X+1)}]in {5,10,...,20}

    {coordinate (aux1) at ($(mat-1-Y.west)!0.5!(mat-1-X.east)$);

    coordinate (aux2) at (mat-X-1.south);

    draw (mat.north -| aux1) -- (mat.south -| aux1)

    (mat.west |- aux2) -- (mat.east |- aux2);}

    foreach X/Y [evaluate=Y as Z using {int(Y+3)}] in

    {6/2,5/6,11/7,10/12,16/12,20/22} 

    {draw[very thick, dots=8 per 1cm,shorten >=3pt,shorten <=3pt]

    (mat-Y-X) -- (mat-Z-X);}

    draw[line width=1.2mm, dots=4 per 1cm]

    (mat-16-18.center) -- (mat-18-20.center)

    (mat-18-16.center) -- (mat-20-18.center);

end{tikzpicture}

end{document}