Spalign package: the use of square brackets with the borders

Question

I am curious, since I have done several tests, how to set up the square brackets for the first matrix when I use the border with spalign package. I have seen this question and....actually I am not able to do it.

Better spacing around brackets of kbordermatrix

\documentclass[a4paper,12pt]{article}
\usepackage{spalign}
\begin{document}
\[\def\spalignendline{\cr}
\spalignrun{\bordermatrix{\the\spaligntoks}}
{, \scriptstyle{1} \scriptstyle{2}; \scriptstyle{1} 0 1; \scriptstyle{2} 1 0}\times \spaligndelims{[}{]} \spalignmat{a b; c d}=\spaligndelims{\{}{\}} \spalignmat{r t; s w}\]
\end{document}

Answer 1

The parentheses are hard-coded in \bordermatrix. You could define a version with brackets explicitly as shown in \bordermatrix with brackets [ ] instead of parentheses ( ).

Alternatively, let us be lazy, copy the definition of \bordermatrix, and let xpatch replace the parentheses by brackets.

\documentclass[a4paper,12pt]{article}
\usepackage{spalign}

\usepackage{xpatch}
\let\bbordermatrix\bordermatrix
\xpatchcmd{\bbordermatrix}{(}{[}{}{}
\xpatchcmd{\bbordermatrix}{)}{]}{}{}

\begin{document}
\[
\def\spalignendline{\cr}\spaligndelims{[}{]}
\spalignrun{\bbordermatrix{\the\spaligntoks}}
{, \scriptstyle{1} \scriptstyle{2}; \scriptstyle{1} 0 1; \scriptstyle{2} 1 0}
\times
\spaligndelims{[}{]} \spalignmat{a b; c d}
=
\spaligndelims{\{}{\}} \spalignmat{r t; s w}
\]
\end{document}

Answer 2

For information, in nicematrix, you can easily write a command \lightmatrix to compose matrices with the syntax of spalign (thanks to the key light-syntax inspired by spalign) with the ability to use all the features of nicematrix, included exterior rows and columns (inspired by \bordermatrix and kbordermatrix).

\documentclass{article}
\usepackage{nicematrix}

\begin{document}

\ExplSyntaxOn
\NewDocumentCommand { \lightmatrix } { D < > { p } O { } m } 
  {
    \group_begin:
    \NiceMatrixOptions { light-syntax }
    \begin { #1 NiceMatrix} [ #2 ]
    #3
    \end { #1 NiceMatrix }
    \group_end:
  }
\ExplSyntaxOff

\NiceMatrixOptions
  {
    code-for-first-row = \scriptstyle, 
    code-for-first-col = \scriptstyle,
  }

$\lightmatrix<b>[first-row,first-col]{ {}  1  2 ; 1  0  1 ; 2 1 0 }
\times
\lightmatrix{a  b ; c  d}
= 
\lightmatrix<B>{r  t ; s  w}$

\end{document}