Label rows of a matrix by characters

You can use the blkarray package:

\documentclass[12pt]{report}
\usepackage{blkarray}
\usepackage{amsmath}

\begin{document}

\[
\begin{blockarray}{cccccc}
a & b & c & d & e \\
\begin{block}{(ccccc)c}
  1 & 1 & 1 & 1 & 1 & f \\
  0 & 1 & 0 & 0 & 1 & g \\
  0 & 0 & 1 & 0 & 1 & h \\
  0 & 0 & 0 & 1 & 1 & i \\
  0 & 0 & 0 & 0 & 1 & j \\
\end{block}
\end{blockarray}
 \]

\end{document}

Here is an option using kbordermatrix:

\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\usepackage{kbordermatrix}% http://www.hss.caltech.edu/~kcb/TeX/kbordermatrix.sty
\begin{document}
\[
  \begin{array}{l@{{}={}}c}
  \text{Mat}_{\varphi\text{ to }M} & \left(\begin{array}{@{}ccccc@{}}
    1 & 1 & 1 & 1 & 1 \\
    0 & 1 & 0 & 0 & 1 \\
    0 & 0 & 1 & 0 & 1 \\
    0 & 0 & 0 & 1 & 1 \\
    0 & 0 & 0 & 0 & 1
  \end{array}\right)
  \end{array}
\]

\renewcommand{\kbldelim}{(}% Left delimiter
\renewcommand{\kbrdelim}{)}% Right delimiter
\[
  \text{Mat}_{\varphi\text{ to }M} = \kbordermatrix{
    & c_1 & c_2 & c_3 & c_4 & c_5 \\
    r_1 & 1 & 1 & 1 & 1 & 1 \\
    r_2 & 0 & 1 & 0 & 0 & 1 \\
    r_3 & 0 & 0 & 1 & 0 & 1 \\
    r_4 & 0 & 0 & 0 & 1 & 1 \\
    r_5 & 0 & 0 & 0 & 0 & 1
  }
\]

\end{document}

For more options and styles, including the usage of \bordermatrix, see Where is the \matrix command?

I'll add a variant with blockarray, with footnote size text as column and row headings (answer to another, duplicate question):

\documentclass{article}
\usepackage{mathtools}
\usepackage{blkarray, bigstrut} %

\begin{document}

\begin{equation*}
  \mathbf{S}=
  \begin{blockarray}{*{5}{c} l}
    \begin{block}{*{5}{>{$\footnotesize}c<{$}} l}
      Rose & Teal & Plum & Sand & Peach & \\
    \end{block}
    \begin{block}{[*{5}{c}]>{$\footnotesize}l<{$}}
      0 & 9 & 8 & 0 & 7 \bigstrut[t]& small \\
      3 & 5 & 6 & 5 & 1 & medium \\
      1 & 0 & 0 & 3 & 2 & large \\
    \end{block}
  \end{blockarray}
\end{equation*}

\end{document}