Drawing this matrix using Tikz

For fun: that is easy with pstricks:

\documentclass[11pt,x11names]{standalone}
\usepackage{pst-node}
\usepackage{auto-pst-pdf}
\usepackage{amsmath}
\usepackage{sansmath}

\begin{document}

 \mathversion{sans}\setlength\fboxsep{0pt}
\begin{postscript}
    $\begin{pmatrix}
        0 & 0 & 0 & 0 & \dots & 0 \\ 0 & \pnode[0,1.5ex]{A} & & &\pnode[0,1.5ex]{Dh} \\0\\0\\\vdots &\pnode{Dv} \\0 & & & & & \pnode{B}
    \end{pmatrix}$
    \psset{arrowinset=0, linewidth=1.5pt, linearc=0.2pt, nodesep = 6pt,, arrows =c- }
    \psline{<->}(A)(B)
    \psset{linecolor=RoyalBlue2, fillcolor=RoyalBlue1!15!, arrows =c-}
    \ncangle[angleB=90, linestyle = none, fillstyle=solid,]{A}{B}
    \ncline[nodesepB=9.5pt]{A}{Dh}
    \ncangle[angleA=90, nodesepB=7.5pt]{B}{Dh}
    \rput(Dh){\color{RoyalBlue2}\dots}
    \psset{angleA=-90, angleB=180, linecolor=Red1!60!, fillcolor=Red1!10!, arrows =-c}
    \ncangle[linestyle=none, fillstyle=solid]{A}{B}
    \ncangle[nodesepA=3pt,]{Dv}{B}
    \ncline[nodesepA=12pt]{Dv}{A}
    \rput[B](Dv){\color{Red1!60!}\vdots}
\end{postscript}

\end{document} 

With TikZ is easy to:

\documentclass[border=3mm,
               tikz,
               prewiev]{standalone}
\usetikzlibrary{matrix}
\begin{document}
    \begin{tikzpicture}
\matrix[matrix of math nodes,
        left delimiter=(,
        right delimiter=),
        nodes in empty cells] (m)
{
0       & 0 & 0 & 0 & \dots & 0 \\
0   & \vphantom{0}  
            &   &   &       &   \\
0       &   &   &   &       &   \\
0       &   &   &   &       &   \\
\vdots  &   &   &   &       &   \\
0       &   &   &   &       &   \\
};
\fill[blue!30] (m-2-2.north west) -| (m-6-6.south east);
\fill[ red!30] (m-2-2.north west) |- (m-6-6.south east);
\draw[line width=3mm,white]  (m-2-2.north west) -- (m-6-6.south east);
\draw[thick,stealth-stealth] (m-2-2.north west) -- (m-6-6.south east);

    \end{tikzpicture}
\end{document}

Edit: Gonzalo Medina remind me on the forgotten dots, Sorry for this. Now I add them in the first row and column and also appearance of diagonal line with use white background line.

Edit (2): The matrix will be centered in text, if you enclose with \begin{center} ... \end{center} or put in some other appropriate environment, for example \begin{figure}\centering\begin{tikzpicture} ... \end{tikzpicture}\end{figure}, etc.

For rounded shadow fill you need to add option rounded corners. Se new MWE below.

\documentclass{article}
    \usepackage{tikz}
\usetikzlibrary{matrix}

\usepackage[active,tightpage]{preview}% just for show only picture
\PreviewEnvironment{center}%
\setlength\PreviewBorder{1em}


\begin{document}
    \begin{center}
    \begin{tikzpicture}
\matrix[matrix of math nodes,
        left delimiter=(,
        right delimiter=),
        nodes in empty cells] (m)
{
0       & 0 & 0 & 0 & \dots & 0 \\
0   & \vphantom{0}
            &   &   &       &   \\
0       &   &   &   &       &   \\
0       &   &   &   &       &   \\
\vdots  &   &   &   &       &   \\
0       &   &   &   &       &   \\
};
\fill[rounded corners,blue!30] (m-2-2.north west) -| (m-6-6.south east);
\fill[rounded corners, red!30] (m-2-2.north west) |- (m-6-6.south east);
\draw[line width=3mm,white]  (m-2-2.north west) -- (m-6-6.south east);
\draw[thick,stealth-stealth] (m-2-2.north west) -- (m-6-6.south east);
    \end{tikzpicture}
    \end{center}
\end{document}