Labelling Ax = b under an actual Matrix

Question

I wish to achieve the following in Latex:

| a b | x | x1 | = | b1 |
| c d |   | x2 |   | b2 |
   A         x       b

Where I write the labels A, x, and b under the respective matrices. The code I'm using to write the Matrices is (feel free to improve the my code -- I am suffering from over a decade of LateX abstinence).

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align}
\begin{pmatrix}
    a & b \\
    c & d
\end{pmatrix}
\times
\begin{pmatrix}
    x1 \\
    x2
\end{pmatrix}
=
\begin{pmatrix}
    b1  \\
    b2 
\end{pmatrix}
\end{align}
\end{document}

Thanks.

Answer 1

Here's a perhaps better version, with a new environment which accepts the subscript as argument:

\documentclass{article}
\usepackage{amsmath}

\newenvironment{spmatrix}[1]
 {\def\mysubscript{#1}\mathop\bgroup\begin{pmatrix}}
 {\end{pmatrix}\egroup_{\textstyle\mathstrut\mysubscript}}

\begin{document}
\begin{equation}
\begin{spmatrix}{A}
    a & b \\
    c & d
\end{spmatrix}
\begin{spmatrix}{x}
    x_1 \\
    x_2
\end{spmatrix}
=
\begin{spmatrix}{b}
    b_1  \\
    b_2
\end{spmatrix}
\end{equation}
\end{document}

Note: too big subscripts may cause misalignment.

I wouldn't use \times for matrix multiplication: no symbol is generally used.

Also align for a single equation is wrong.

---

If someone is asking why the \def\mysubscript{#1} bit in the definition, the answer is that LaTeX doesn't allow using #1 in the "end" part of \newenvironment. This limitation does not hold with xparse:

\usepackage{xparse}
\NewDocumentEnvironment{spmatrix}{ m }
  {\mathop\bgroup\begin{pmatrix}}
  {\end{pmatrix}\egroup_{\textstyle\mathstrut #1}}

Answer 2

It can be achieved by putting the matrix and the vectors inside \mathop. The example also uses \textstyle for a larger size and \vphantom for adjusting the baselines.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align}
\mathop{\begin{pmatrix}
    a & b \\
    c & d
\end{pmatrix}}_{\textstyle A} 
\times
\mathop{\begin{pmatrix}
    x1 \\
    x2
\end{pmatrix}}_{\textstyle x\vphantom{A}}
=
\mathop{\begin{pmatrix}
    b1  \\
    b2
\end{pmatrix}}_{\textstyle b\vphantom{A}}
\end{align}
\end{document}

Addition: Macro form.

\documentclass{article}
\usepackage{amsmath}
\newcommand*{\putunder}[2]{%
  {\mathop{#1}_{\textstyle #2}}%
}
\begin{document}
\begin{gather}
\putunder{
  \begin{pmatrix}
    a & b \\
    c & d
  \end{pmatrix}
}{A}
\times
\putunder{
  \begin{pmatrix}
    x1 \\
    x2
  \end{pmatrix}
}{x\vphantom{A}}
=
\putunder{
  \begin{pmatrix}
    b1  \\
    b2
  \end{pmatrix}
}{b\vphantom{A}}
\end{gather}
\end{document}

Answer 3

Here is one that abuses a feature of mathtools (a supplement and some correction to amsmath features. Check the documentation) which I use often. It's actually drawing a bracket but zeroing it's linewidth makes it invisible. It's not elegant but still I didn't have any problems yet (doesn't mean I won't).

The command is \underbracket[<rule thickness>] [<bracket height>]{<arg>}

\documentclass{article}
\usepackage{mathtools}
\begin{document}
\[
\underbracket[0pt][0pt]{%
\begin{pmatrix}
    a & b \\
    c & d
\end{pmatrix}}_{\mathstrut A}
\times
\underbracket[0pt][0pt]{%
\begin{pmatrix}
    x_1 \\
    x_2
\end{pmatrix}}_{\mathstrut x}
=
\underbracket[0pt][0pt]{%
\begin{pmatrix}
    b_1  \\
    b_2 
\end{pmatrix}}_{\mathstrut b}
\]
\end{document}

The contents of the labels are top aligned so I've pushed the x label a bit down. Thanks to egreg, now the contents are fixed to the baseline regardless of their height.

Answer 4

Another option is to use \underset as in this answer.

Code

[Edit: added \usepackage{amsmath}]

\documentclass{article}
\usepackage{amsmath}
\begin{document}
$\underset{\begin{array}{c}\\ A \end{array}}%
{%
\begin{pmatrix}
    a & b \\ 
    c & d%
\end{pmatrix}%
}%
\underset{\begin{array}{c}\\ x \end{array}}%
{%
\begin{pmatrix}
    x_{1} \\ 
    x_{2}%
\end{pmatrix}%
}=\underset{\begin{array}{c}\\ b \end{array}}%
{%
\begin{pmatrix}
    b_{1} \\ 
    b_{2}%
\end{pmatrix}%
          }$
\end{document}

Output

Answer 5

In plain TeX I would use \atop:

$$
{\pmatrix{a  &b \cr c &d\cr}\atop A}
{\pmatrix{x_1\cr x_2}\atop \mathstrut x}
\raise8pt\hbox{=} {\pmatrix{b_1\cr b_2}\atop b}
$$
\bye

but I had to manually adjust the position of the equal sign.

Answer 6

Just to have an overkilling solution with TikZ...

\documentclass{article}
\usepackage{amsmath,tikz}            
\usetikzlibrary{matrix,positioning}

\def\vertmathalign{-\the\dimexpr\fontdimen22\textfont2\relax}

\tikzset{rnd delim matrix/.style={
        left delimiter=(,right delimiter=),
         ampersand replacement=\&, inner sep=1pt,
         every node/.style={anchor=base},row sep=0.75ex,
         column sep=0.5em,matrix of math nodes,
         minimum height=2ex,
    }
}

\tikzset{math node/.style={
        execute at begin node={$},
        execute at end node={$},
        text height=1ex,
    }
}

\begin{document}

\begin{align}
\begin{tikzpicture}[baseline=\vertmathalign]
\matrix (m1)[rnd delim matrix]{
a \& b \\
c \& d \\
};
\node[math node,below=0.15cm of m1]{A};
\end{tikzpicture}
\begin{tikzpicture}[baseline=\vertmathalign]
\matrix (m2)[rnd delim matrix]{
x_1\\
x_2\\
};
\node[math node,below=0.2cm of m2]{x};
\end{tikzpicture}
=
\begin{tikzpicture}[baseline=\vertmathalign]
\matrix (m3)[rnd delim matrix]{
b_1\\
b_2\\
};
\node[math node,below=0.15cm of m3]{b};
\end{tikzpicture}
\end{align}

\end{document}

The result: