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I want to draw the following diagram which contains two matrices (2x2 on left and 4x4 on right) and a box. Could someone help?

With some motivations from @Alain Matthes answer: Tikz: Arrowheads in the center

This could be a starting point for your quest:

documentclass{article}

usepackage{amsmath}

usepackage{tikz}

usetikzlibrary{arrows}

usetikzlibrary{decorations.markings}



begin{document}

pagestyle{empty}

%

tikzstyle{int}=[draw, minimum size=2em]

tikzset{->-/.style={decoration={

            markings,

            mark=at position #1 with {arrow{>}}},postaction={decorate}}}

begin{tikzpicture}[node distance=2.5cm, auto]

    node [int] (a) {DST};

    node (b) [left of=a, coordinate] {a};

    node (c) [right of=a, coordinate] {a};

    draw[dashed, ->-=0.5] (b) --(a);   

    draw[dashed, ->-=0.5] (a) --(c);   

    node        (d) [right of=c,shift={(-1.1cm,0mm)}]{$begin{pmatrix}

        c&c&v&b\

        a&b&c&d\

                a&b&c&d\

                        a&b&c&d

        end{pmatrix}$};

    node        (e) [right of=b, shift={(-3.1cm,0mm)}]{$begin{pmatrix}

        c&c\

        a&b

        end{pmatrix}$};    

end{tikzpicture}



end{document}

which would give:

Note: Since your arrows are not aligned in the center, I used the macro option from the answer to play with the placement of the arrows as you define. For more information on how-to, please refer the link given above.

Rather similar to Raaja's nice answer except that I am using tikzmark to annotate an ordinary equation, such that identations are unchanged. And the TikZ path can be done in one stroke.

documentclass[fleqn]{article}

usepackage{amsmath}

usepackage{tikz}

usetikzlibrary{tikzmark}

usetikzlibrary{decorations.markings}

% from https://tex.stackexchange.com/a/39282/121799

tikzset{->-/.style={decoration={

            markings,

            mark=at position #1 with {arrow{>}}},postaction={decorate}}}

begin{document}

[

tikzmarknode{L}{begin{pmatrix}

 1 & 2 \ 3 & 4

end{pmatrix}}

qquadqquadqquadqquadqquadqquad

tikzmarknode{R}{begin{pmatrix}

 1 & 2 & 3 & 4 \

 5 & 6 & 7 & 8 \

 9 & 10 & 11 & 12 \

 13 & 14 & 15 & 16 \

end{pmatrix}}

]

begin{tikzpicture}[overlay,remember picture]

 draw[>=latex,dashed,->-=0.2,->-=0.8] (L) -- (R)

 node[midway,fill=white,draw,solid]{DST};

end{tikzpicture}

end{document}