Vertically align the tops of matrices in an equation

A note before, amsmath provides special *matrix environments:

• pmatrix for ( · )
• bmatrix for [ · ]
• Bmatrix for { · }
• vmatrix for | · |
• Vmatrix for || · ||

Solution 1

I used the \vphantom macro that resizes the box inside the \overset to same height like the other parts.

Code

\documentclass{article}
\usepackage{amsmath}
\newcommand*\biggestpart{}
\begin{document}
\renewcommand*\biggestpart{
  \begin{bmatrix}
    t_1    & 1 \\
    \vdots & \vdots \\
    t_n    & 1
  \end{bmatrix}
}
\begin{align*}
\overset{A}{\biggestpart}
\overset{x}{
  \vphantom{\biggestpart}
  \begin{bmatrix}
    x_1 \\ x_2
  \end{bmatrix}
}
&=
\overset{b}{
  \begin{bmatrix}
    b_1 \\ \vdots \\ b_n
  \end{bmatrix}
}
\end{align*}
\end{document}

Output

Solution 2

As the second row in the bigger matrices are not of the same height of x_2 the \vphantom command is used again (try it without to see the effect or replace \vdots with “normal” math stuff like x_0).

Code

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
\overset{A}{
  \begin{bmatrix}
    t_1    & 1 \\
    \vdots & \vdots \\
    t_n    & 1
  \end{bmatrix}}
\overset{x}{
\begin{array}{@{}c@{}}{
  \begin{bmatrix}
    x_1 \\ x_2 \vphantom{\vdots}
  \end{bmatrix}}\\
  \\
  \end{array}
}
&=
\overset{b}{
  \begin{bmatrix}
    b_1 \\ \vdots \\ b_n
  \end{bmatrix}
}
\end{align*}
\end{document}

Output

Here is a sans-amsmath version of Qrrbrbirlbel's answer:

\documentclass{article}
\newcommand{\matlabel}[2]{% \matlabel{<label>}{<stuff>}
  \begin{array}{@{}c@{}} \mbox{\small$#1$} \\ #2 \end{array}
}
\begin{document}
\[
  \matlabel{A}{\left[\begin{array}{@{}cc@{}}
      t_1 & 1 \\
      \vdots & \vdots \\
      t_n & 1
    \end{array}\right]}
  \matlabel{x}{\left[\begin{array}{@{}c@{}}
      x_1 \\ \vphantom\vdots x_2 \\
    \end{array}\right] \\
    \mathstrut}\mathrel{\raisebox{-.5\normalbaselineskip}{=}}
  \matlabel{b}{\left[\begin{array}{@{}c@{}}
      b_1 \\ \vdots \\ b_n
    \end{array}\right]}
\]
\end{document}

The only major difference is the setting of the matrix label as an element in an "vertical array", rather than an "upper limit in a math operator." As a consequence, the vertical alignment with respect to the mathematical axis has to be adjusted... using \mathrel{\raisebox{-.5\normalbaselineskip}{=}}.