Highlighting rows/columns/diagonals in matrix

Question

I'm trying to highlight rows/columns/diagonals in a matrix. I came across this example, which looks very clean. Unfortunately, it seems to cause some issue with spacing in the matrix, and I can't figure out why. Below is a MWE and the output:

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}

\newcommand{\tikzmark}[2]{
    \tikz[overlay,remember picture,baseline] 
    \node[anchor=base] (#1) {$#2$};
}

\begin{document}

No highlighting:
\begin{equation}
  A =
  \begin{bmatrix}
    a_{11} & 0 & 0 \\
    0 & a_{22} & 0 \\
    0 & 0 & a_{33}\\
  \end{bmatrix}
\end{equation}

Highlighting:
\begin{equation}
  A =
  \begin{bmatrix}
    \tikzmark{top}{a_{11}} & 0 & 0 \\
    0 & a_{22} & 0 \\
    0 & 0 & \tikzmark{bottom}{a_{33}}\\
  \end{bmatrix}
\end{equation}
\begin{tikzpicture}[overlay,remember picture]
  \draw[opacity=.4,line width=3mm,line cap=round] (top.center) -- (bottom.center);
\end{tikzpicture}

\end{document}

What is the \tikzmark command doing, and is there anything that can be done to preserve the standard matrix spacing?

Answer 1

Here is a version with the tikzmark library (and the eso-pic package to get the highlighting on the background).

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{tikzmark,calc}
\usepackage{eso-pic}
\begin{document}

No highlighting:
\begin{equation}
  A =
  \begin{bmatrix}
    a_{11} & 0 & 0 \\
    0 & a_{22} & 0 \\
    0 & 0 & a_{33}\\
  \end{bmatrix}
\end{equation}

Highlighting:
\begin{equation}
  A =
  \begin{bmatrix}
    \tikzmarknode[circle]{top}{a_{11}} & 0 & 0 \\
    0 & a_{22} & 0 \\
    0 & 0 & \tikzmarknode[circle]{bottom}{a_{33}}\\
  \end{bmatrix}
\end{equation}
\AddToShipoutPictureBG*{%
\begin{tikzpicture}[overlay,remember picture]
  \draw let  \p1=($(top.north)-(top.center)$),
  \p2=($(bottom.north)-(bottom.center)$), \n1={2*max(\y1,\y2)-2pt} in
  [opacity=.4,line width=\n1,line cap=round,
  shorten >=-\y2/3,shorten <=-\y1/3] (top.center) -- (bottom.center);
\end{tikzpicture}}
\end{document}

Answer 2

An adapt with variants of the nice answer of @Zarko Rectangle box around elements of matrix using nicematrix package as also suggested by the very good user @Schrödinger's cat in your comment. If you want to have more rounded corners increase the parameter rounded corners=2pt. I add a MWE and a screenshot:

\documentclass[12pt]{article}
\usepackage{nicematrix,tikz}
\usetikzlibrary{fit}
\begin{document}
\[
\begin{bNiceArray}{>{\strut}ccc}[margin]    
a_{11} & 0 & 0 \\
0 & a_{22} & 0 \\
0 & 0 & a_{33} 
\CodeAfter 
\tikz
\node [fill=gray, rounded corners=2pt, opacity=0.2, 
       rotate fit=-31, inner xsep=1.2pt, inner ysep = -0.8pt,
       fit = (1-1) (3-3)] {} ;
\end{bNiceArray}
\]
\end{document}