For the vertical braces, you can use the bigdelim
package; the horizontal braces were made using \underset
and \underbrace
and a "rule" of variable width and no height:
\documentclass{article}
\usepackage{amsmath}
\usepackage{easybmat}
\usepackage{multirow,bigdelim}
\newcommand*\hexbrace[2]{%
\underset{#2}{\underbrace{\rule{#1}{0pt}}}}
\begin{document}
\[
M(z)=
\begin{array}{c@{}c}
\left[
\begin{BMAT}[5pt]{c|c}{c}
\begin{BMAT}[5pt]{c:c:c}{ccccccc}
& & \\
& & \\
& & \\
v_1 & \dots & v_m \\
& & \\
& & \\
& &
\end{BMAT}
&
\begin{BMAT}{c}{c|c}
\begin{BMAT}[5pt]{c:c:c}{ccc}
& & \\
w_1(a) & \dots & w_n(a) \\
& &
\end{BMAT}
\\
\begin{BMAT}[10pt]{c}{c}
B(z)
\end{BMAT}
\end{BMAT}
\end{BMAT}
\right]
&
\begin{array}{l}
\\[-8mm] \rdelim\}{4}{6mm}[$J$] \\ \\ \\[4mm] \rdelim\}{3}{6mm}[$H$] \\ \\
\end{array} \\[-1ex]
\hexbrace{2.7cm}{m}\hexbrace{3.8cm}{n}
\end{array}
\]
\end{document}
If not closed, then this might as well have an answer. Here are a few ways of producing, for example, the second matrix above:
\documentclass{article}
\usepackage{blkarray}
\usepackage{amsmath}
\begin{document}
\[
\begin{blockarray}{ccc}
& U &\\
\begin{block}{[ccc]}
u_{1,1} & \cdots & u_{1,r}\\
\vdots & \ddots & \vdots\\
u_{m,1} & \cdots & u_{m,r}\\
\end{block}
& m\times r& \\
\end{blockarray}
\]
\[
\begin{array}{c}
U\\
\left[\begin{array}{ccc}
u_{1,1} & \cdots & u_{1,r}\\
\vdots & \ddots & \vdots\\
u_{m,1} & \cdots & u_{m,r}\\
\end{array}\right]\\
m\times r
\end{array}
\]
\[
\begin{array}{c}
U\\
\begin{bmatrix}
u_{1,1} & \cdots & u_{1,r}\\
\vdots & \ddots & \vdots\\
u_{m,1} & \cdots & u_{m,r}\\
\end{bmatrix}\\
m\times r
\end{array}
\]
Which give, respectively:
To my eye, the third option produces the best spacing. However, the second two methods work only by virtue of the underset and overset text being in the center column. If it were in a different column, then the first method might be modified to give better spacing, or one of the answers linked in the comments might be preferable.
Best Answer
In today's I have too much free time episode we will attack a question posted without a MWE. Absence of a MWE gives us the right to go as esoteric as possible hence here is one Tweak this, tweak that possibility.