Vertical vectors in angle brackets

Here's a TikZ solution. Not sure I'd recommend it, and it would probably need a little tweaking with regard to spacing as well.

\documentclass{standalone}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{calc}
\usepackage{environ}

\NewEnviron{angmatrix}{%
  \tikz[baseline=0pt]
    \draw[line width=1pt] 
     node[append after command={
      (\tikzlastnode.north west) -- ($(\tikzlastnode.west)+.2*(\tikzlastnode.west)!1!90:(\tikzlastnode.north west)$) -- (\tikzlastnode.south west)
      (\tikzlastnode.north east) -- ($(\tikzlastnode.east)+.2*(\tikzlastnode.east)!1!270:(\tikzlastnode.north east)$) -- (\tikzlastnode.south east)
      }] {\(\begin{matrix} \BODY \end{matrix}\)};}%
{}


\begin{document}
\[
A = 
\begin{angmatrix}
  a \\ b \\ c \\ d \\ e \\ f \\ g
\end{angmatrix}, B = 
\begin{angmatrix}
  a \\ b \\ c
\end{angmatrix}, C = 
\begin{angmatrix}
  a
\end{angmatrix}
\]
\end{document}

Result:

Adding \usepackage{yhmath} sorts this for me (see texdoc yhmath for details)

\documentclass{article}
\usepackage{amsmath}
\usepackage{yhmath}
\begin{document}

$
\left\langle
    \begin{matrix}
      a  \\
      b  \\
      c  \\
      d  \\
    \end{matrix}
\right\rangle
$

\end{document}

I have added this as a second solution, based on @mico's comment to my earlier solution. It uses a non-free but no-cost font, MTPro2 Lite from PCTeX.

The use of the font to produce large delimiters needs a different syntax as well as loading the font (if a regular user of MTPro2 knows better, please let us know). Unlike \yhmath these delimiters can scale to very large matrices (up to 4 inches high, according to the documentation). The syntax is described in detail in section 2.12 of the MTPro2 LaTeX Guide. For example:

\documentclass{article}
\usepackage{amsmath}
\usepackage[lite]{mtpro2}
\begin{document}
$\LEFTRIGHT\langle\rangle{
   \begin{matrix}
      a  \\
      b  \\
      c  \\
      d  \\
      e  \\
      f  \\
      g  \\
      h  \\
    \end{matrix}}$
$\LEFTRIGHT\langle\rangle{
   \begin{matrix}
      a  \\
      b  \\
      c  \\
      d  \\
    \end{matrix}}$
\end{document}