Writing "stochastic matrices" in LaTeX

Question

I'm having some notes on stochastic processes and would like to know if there is a less painful way to build stochastic matrices in LaTeX. By painful I want to continue the way I did below.

Question. Is there a more straightforward and economical way to write stochastic matrices in LaTeX? Stochastic matrices have indices above and to the left of matrz aligned with the rows and columns of the matrix. The only way I found to make such an array is by manually adjusting the alignment as in the code below.

$$
\begin{array}{cc ccc c ccc c}
&
& 
\hspace*{-5mm}1
&
2
&
3
&
\cdots
&
b-2
&
b-1
&
b
\\
\\
    \begin{array}{c}
    0\\1\\2\\\vdots \\ \\\vdots \\ b-1 \\ b  
    \end{array}
& 
    \left[
    \begin{array}{c}
    \\ \\ \\ \\  \\ \\  \\  \\   
    \end{array}
    \right.
&\hspace*{-4mm}
    \begin{array}{c}
    1\\q\\0\\\vdots \\ \\\vdots \\ 0 \\ 0  
    \end{array}
&
    \begin{array}{c}
    0\\r\\q\\\vdots \\ \\\vdots \\ 0 \\ 0  
    \end{array}
&
    \begin{array}{c}
    0\\0\\p\\\vdots \\ \\\vdots \\ 0 \\ 0  
    \end{array}
&
    \begin{array}{c}
    \cdots \\ \cdots\\ \cdots \\\vdots \\ \\\vdots \\\cdots\\ \cdots  
    \end{array}
&
    \begin{array}{c}
    0 \\ 0\\ 0 \\\vdots \\ \\\vdots \\q\\ 0  
    \end{array}
&
    \begin{array}{c}
    0 \\ 0\\ 0 \\\vdots \\ \\\vdots \\r\\ 0  
    \end{array}
&
    \begin{array}{c}
    0 \\ 0\\ 0 \\\vdots \\ \\\vdots \\p\\ 1  
    \end{array}
&\hspace*{-4mm} 
    \left.
    \begin{array}{c}
    \\ \\ \\ \\  \\ \\  \\  \\   
    \end{array}
    \right]
\end{array}
$$

Unrelated: don't use $$ ...$$ for display math in LaTeX, see Why is \[ … \] preferable to $$? — Torbjørn T., May 06 '18 at 19:07
The title makes it seems as if you want LaTeX to randomize the matrices. Consider removing the "Stochastic" word by [edit]ing the title. — Andreas Storvik Strauman, May 06 '18 at 19:10
kbordermatrix or blkarray perhaps: https://tex.stackexchange.com/questions/30791/array-with-labeling-columns?noredirect=1&lq=1 — Torbjørn T., May 06 '18 at 19:10

score 4 · Accepted Answer · answered May 06 '18 at 20:28

With blkarray you still need some adjustments, not so much as with your code.

\documentclass{article}
\usepackage{amsmath}
\usepackage{blkarray}

\begin{document}

\[
\begin{blockarray}{ *{8}{c} }
& 1 & 2 & 3 & \dots & b-2 & b-1 & b \\
\begin{block}{ c @{\quad} [ @{\,} *{7}{c} @{\,} ] }
0 & 1 & 0 & 0 & \dots & 0 & 0 & 0 \smash[b]{\vphantom{\Big|}} \\
1 & q & r & 0 & \dots & 0 & 0 & 0 \\
2 & 0 & q & p & \dots & 0 & 0 & 0 \\
\vdots & \vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \vdots \\
b-1 & 0 & 0 & 0 & \dots & q & r & p \\
b & 0 & 0 & 0 & \dots & 0 & 0 & 1 \smash[t]{\vphantom{\Big|}} \\
\end{block}
\end{blockarray}
\]

\end{document}

score 3 · Answer 2 · answered Sep 06 '23 at 18:35

With {NiceMatrix} of nicematrix which has tools designed to address that kind of problem.

\documentclass{article}
\usepackage{nicematrix}
\begin{document}
[
\begin{NiceMatrix}
  & 1 & 2 & 3 & \dots & b-2 & b-1 & b \
  0 & 1 & 0 & 0 & \dots & 0 & 0 & 0 \
  1 & q & r & 0 & \dots & 0 & 0 & 0 \
  2 & 0 & q & p & \dots & 0 & 0 & 0 \
  \vdots & \vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \vdots \
  b-1 & 0 & 0 & 0 & \dots & q & r & p \
  b & 0 & 0 & 0 & \dots & 0 & 0 & 1 \
\CodeAfter
  \SubMatrix[{2-2}{7-8}]
\end{NiceMatrix}
]
\end{document}

I should rewrite all my answers with blkarray in terms of nicemetrix before you take over them. Just joking and +1 — egreg, Sep 06 '23 at 20:03

Writing "stochastic matrices" in LaTeX

2 Answers2