How to programmatically insert an \hline between each line of an array

Question

I'm trying to create an environment for matrices that are divided in four sections, such as the following:

Ideally, I'd like to make it so that it can be used like the following:

M = 
\left(
\begin{croosmatrix}
   \begin{matrix}
      a & b & c & d \\
      e & f & g & h \\
      i & j & k & l 
   \end{matrix} 
      & B \\
   C & D \\
\end{crossmatrix}
\right)

I already know how to achieve such result manually, as decribed in Dividing line in a matrix. Something like the following:

M = 
\left(
\begin{array}{c|c}
   \begin{matrix}
      a & b & c & d \\
      e & f & g & h \\
      i & j & k & l 
   \end{matrix} 
      & B \\
   \hline
   C & D \\
\end{array}
\right)

My question is, how could I make it an environment? In other words, is there a way to programmatically place an \hile between each like on an array? Is it possible to create an environment for such a thing?

Answer 1

You can use nicematrix which constructs the matrix while creating Tikz nodes. You can use these nodes to draw what you want with Tikz.

\documentclass{article}
\usepackage{nicematrix,tikz}
\NewDocumentEnvironment {crossmatrix} { }
  { \begin{pNiceArray}{cc}[margin] }
  {
    \CodeAfter
    \tikz \draw (2-|1) -- (2-|3) (1-|2) -- ([yshift=1pt]2-|2) ++ (0,-2pt) -- (3-|2) ;
    \end{pNiceArray}
  }
\begin{document}
$M = 
\begin{crossmatrix}
   \begin{matrix}
      a & b & c & d \
      e & f & g & h \
      i & j & k & l 
   \end{matrix}
      & B \
   C & D 
\end{crossmatrix}$
\end{document}

Answer 2

You want to insert to the item of the outer table (\halign) the nested table (\haling). It is not problem if the nested \halign is realized as a macro which reads its parameter in {...}. Then such parameter can include tabs & and \cr used for its inner nested \halign. But if you want to use a macro with separated parameter and not in {...} then the tabs & and \cr in such parameter are interpreted during reading of the parameter as tabs for outer \halign.

The nested \begin{matrix}..&..&.\end{matrix} reads its parameter terminated by \end{matrix} (no in {...}), so tabs & used here are interpreted by the outer \halign. Of course, you can hide these tabs by {\begin{mattrix}..&..&.\end{matrix}} but the LaTeX logic of tagging tables and using nested LaTeX environments is lost.

The following example shows the problem in native TeX language:

\def\a#1{\vbox{\halign{##&##\cr#1\cr}}}

\halign{X#Y&Z#W\cr    ..\a{b&c}..& d\cr}

Works, because the b&c is read inside {}, so the & here is not interpreted by the outer \halign.

\def\a[#1]{\vbox{\halign{##&##\cr#1\cr}}}

\halign{X#Y&Z#W\cr    ..\a[b&c]..& d\cr}

Doesn't work because when b& is read into the parameter then TeX interprets & as the tab for outer \halign and the reading of the parameter continues by Y followed by \endtemplate which is prohibited read it to a parameter.

\def\a[#1]{\vbox{\halign{##&##\cr#1\cr}}}

\halign{X#Y&Z#W\cr    ..{\a[b&c]}..& d\cr}

Works.

Answer 3

The problem is the syntax. Here I propose to specify the parts as arguments to the environment.

\documentclass{article}
\usepackage{amsmath}

\newenvironment{crossmatrix}[3]
 {
  \left(
  \def\crossmatrixfinal{&#1\\\hline#2&#3}
  \begin{array}{@{}c|c@{}}
  \begin{matrix}
 }
 {
  \end{matrix}
  \crossmatrixfinal
  \end{array}
  \right)
 }

\begin{document}

\[
\begin{crossmatrix}{B}{C}{D}
  a & b & c & d \\
  e & f & g & h \\
  i & j & k & l 
\end{crossmatrix}
\]

\end{document}