matrices
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.
One way to do this is implemented in the (free, in both senses!) online linear algebra textbook Linear Algebra by Jim Hefferon. It's written in LaTeX and is open-source so one can download the book and its attendant style files. One of them, called linalgjh.sty is about typesetting common linear algebra stuff such as augmented matrices and row reductions and the like. The code for the augmented matrices is:
\newenvironment{amatrix}[1]{%
\left(\begin{array}{@{}*{#1}{c}|c@{}}
}{%
\end{array}\right)
}
and is used as:
\begin{amatrix}{2}
1 & 2 & 3 \\ a & b & c
\end{amatrix}
(note that the argument is one less than the total number of columns). I guess that the @{}s at the start and end are to get the spacing right with the parentheses (mentioned by TH in a comment to fabikw's similar answer).
That style file has several other useful linear algebra macros that may be useful.
The coding of this matrix product is quite straightforward, just take the time to write the four matrices that make up the formula with indexed variables.
\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}
%>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
\begin{equation*}
\begin{pmatrix}
y_1 \\
\vdots \\
y_n
\end{pmatrix}=
\begin{pmatrix}
1 & x_{12} & \ldots & x_{1k} \\
\vdots & \vdots & \ddots & \vdots \\
1 & x_{N2} & \ldots & x_{Nk}
\end{pmatrix}
\begin{pmatrix}
\beta_1 \\
\vdots \\
\beta_k
\end{pmatrix}
+
\begin{pmatrix}
u_1 \\
\vdots \\
u_k
\end{pmatrix}
\end{equation*}
% <<<<<<<<<<<<<<<<<<<<<<<<<<<<<
\end{document}
Best Answer
I would suggest writing something more traditional and clear: