What's the best way to write matrix together with its dimensions on top and left?

Question

I'm trying to show that matrix A (m rows, n columns) times matrix B(n rows, k columns), results as matrix C ( m rows, k columns).

I wonder what's the easier way to write it?

there are several posts here, I found Block matrix equation with dimensioning and Equation with Large Matrix Dimension a bit too complex, while Matrix decomposition dimensions diagram put the dimensions at the bottom of the matrix, while I hope this can be displayed on the left and top.

Answer 1

I would suggest writing something more traditional and clear:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[
  \underset{(m \times n)}{A} \times \underset{(n \times k)}{B} =
    \underset{(m \times k)}{C}
\]
\end{document}

Answer 2

You could use the following code -- note the use of positive thinspace (\,) and negative thinspace (\!) to finetune the position of the side-set and supra-set items.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
$ {}^m\!\overset{\,n}{A} \, {}^n\!\overset{\,k}{B} = {}^m  \overset{\,k}{C} $
\end{document}

Answer 3

A variation of Mico's solution, that's less obtrusive.

The height of the two small superscripts can be changed with an optional argument, in case of need:

\rowcol[<height>]{<matrix>}{<rows>}{<columns>}

\documentclass{article}

\newcommand{\rowcol}[4][2ex]{%
  \raisebox{#1}{\vtop{
    \tiny
    \ialign{%
      &##\cr
      &\rlap{$\,#4$}\cr
      \noalign{\nointerlineskip}
      $#3\!$\cr
    }
  }}
  #2
}

\begin{document}
\[
\rowcol{A}{m}{n}\cdot\rowcol{B}{n}{k}=\rowcol{C}{m}{k}
\]
\end{document}

Answer 4

For a subscript to be put on the top of a given symbol one uses \overset{}{}, where the first blank is to be replaced with the intended subscript and the second blank is to be replaced with the given symbol.

For subscripts to be put on the left or right of a given symbol you may refer to the question here: Left and right subscript / superscript

Hope these helpful.

Answer 5

Another suggestion:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[
  A_{m \times n} B_{n \times k} = C_{m \times k}
\]
\end{document}

EDIT: Or you can simply declare the matrices

and then AB = C. This notation is used, for example, in Golub, Van Loan, "Matrix Computation", 3rd Ed. Johns Hopkins, 1996.