writing two matrices in a clear and nice way

Here's a solution using the matrix library of tikz for the drawing:

Here's the code:

\documentclass[12pt, reqno]{amsart} \usepackage{amsmath,amssymb,amsthm} \usepackage{tikz} % <-- For drawing stuff \usetikzlibrary{matrix, positioning} % <-- For matrix notation and relative positioning \begin{document} \begin{tikzpicture}[ every left delimiter/.style={xshift=0.25cm}, every right delimiter/.style={xshift=-0.15cm} ] \matrix[matrix of math nodes, nodes in empty cells, left delimiter={[ }, right delimiter = { ] }] (matrix) { 0 & & & & & & \\[-0.1cm] & 1 & & & & & \\[-0.1cm] & & 0 & & & & \\[-0.1cm] & & & \frac{1}{2!} & & & \\[-0.1cm] & & & & 0 & & & \\[-0.1cm] & & & & & \frac{1}{3!} & \\[-0.1cm] & & & & & & \ddots \\[-0.1cm] }; \draw[red] ([yshift=0.35cm]matrix-2-1.north west) -- ([xshift=0.05cm]matrix-7-7.260) -- (matrix-7-1.south west) -- cycle node at ([xshift=0.25cm]matrix-5-2)[font=\huge] {0} ; % Lower triangle \draw[red] ([yshift=0.25cm, xshift=-0.25cm]matrix-1-2.north west) -- ([yshift=0.25cm, xshift=0.5cm]matrix-1-7.north east) -- ([xshift=0.25cm, yshift=0.1cm]matrix-7-7.south east) -- cycle node[font=\huge] at (matrix-3-6){0}; % Upper triangle \node[left = 0.25cm of matrix] {\(A = \)}; % text next to matrix % Onto the 2nd matrix now \node[right = 0.0cm of matrix] (mtext) {\(, \ T =\)}; \matrix[matrix of math nodes, nodes in empty cells, left delimiter={[ }, right delimiter = { ] }, right = 0.0cm of mtext] (matrix2) { 0 & 1 & & \\[-0.1cm] & 0 & 1 & \\[-0.1cm] & & \ddots & \ddots \\[-0.1cm] }; \draw[red] ([yshift=0.1cm, xshift=-0.15cm]matrix2-1-1.south) -- ([xshift=0.5cm]matrix2-3-2.south east) -- (matrix2-3-1.south west) -- cycle node[font=\large] at ([yshift=-0.25cm, xshift=0.15cm]matrix2-2-1) {0}; % Lower triangle \draw[red] ([yshift=0.2cm, xshift=-0.25cm]matrix2-1-3.north west) -- ([yshift=0.2cm, xshift=0.25cm]matrix2-1-4.north east) -- ([yshift=-0.25cm]matrix2-3-4.east) -- cycle node[font=\large] at ([yshift=0.25cm, xshift=-0.1cm]matrix2-2-4){0}; % Upper triangle \end{tikzpicture} \end{document} 

As you can tell from the code, building the matrix in tikz allows for very precise control and drawing. You could change/shift every little detail of my drawing to your personal liking. The finetuning potential seems to be endless. It's a worthwhile investment to learn to make matrices with tikz if your matrices involve heavy usage of drawings. Alternatively, the nicematrix package can be used to achieve something similar since it uses tikz under the hood, but I don't know if you can finetune it as much.

A simple solution without additional packages: We first define a "big zero" with null dimensions so that it does not mess up the line spacing, and then place it in an appropriate location in the array.

\documentclass[12pt,reqno]{amsart} \newcommand{\bigo}{\makebox(0,0){\text{\huge 0}}} \begin{document} $$ A= \left[\begin{array}{ccccccc} 0 & & & & & & \\ & 1 & & & & \bigo & \\ & & 0 & & & & \\ & & & \frac{1}{2!} & & & \\ & & & & 0 & & \\ & \bigo & & & &\frac{1}{3!} &\\ & & & & & & \ddots \end{array}\right],\;\, %% T = \left[\begin{matrix} 0 & 1 & &\raisebox{-0.7ex}[0ex][0ex]{\hspace{-2ex}\bigo} \\ & 0 & 1 &\\ \raisebox{2ex}[0ex][0ex]{\hspace{1ex}\bigo} & & \ddots & \ddots \end{matrix}\right]. $$ \end{document} 

Since the second matrix is rather small, there is not much space to add a big zero, so manually adjusting the vertical positioning by \raisebox gives better results. You may actually consider making the matrix larger by repeating a few more diagonal elements.

Here's another way to create diagonal matrix with single 0's at upper and lower triangles. The solution below requires a bit of knowledge of nicematrix and tikz:

The code:

\documentclass{article} \usepackage{tikz} \usepackage{nicematrix} \tikzset{ every node/.style = { inner xsep=0pt, inner ysep=0pt, execute at begin node=\(, execute at end node=\), }, every path/.style = { rounded corners=6pt, }, } \begin{document} \begin{gather} A = \begin{bNiceMatrix} 0 & & & & & & \NotEmpty \\ & 1 & & & & & \\ & & 0 & & & & \\ & & & \frac{1}{2!} & & & \\ & & & & 0 & & \\ & & & & & \frac{1}{3!} & \\ \NotEmpty & & & & & & \ddots \CodeAfter \begin{tikzpicture} \node[ anchor=south west, scale=2.5, ] at (last-1) {0}; \node[ anchor=north east, scale=2.5, ] at (1-last) {0}; \end{tikzpicture} \end{bNiceMatrix} \\[6pt] T = \begin{bNiceMatrix} 0 & 1 & & \NotEmpty \\ & 0 & 1 & \\ \NotEmpty & & \ddots & \ddots \CodeAfter \begin{tikzpicture} \node[ anchor=south west, scale=1.75, xshift=-1pt, ] at (last-1) {0}; \node[ anchor=north east, scale=1.75, yshift=3pt, xshift=2pt, ] at (1-last) {0}; \end{tikzpicture} \end{bNiceMatrix} \end{gather} \end{document} 

EDIT.
The following code will typeset two equations in one line including equation numbers

% ... \begin{equation} A = \begin{bNiceMatrix} % ... the same content \end{bNiceMatrix}, \qquad T = \begin{bNiceMatrix} % ... the same content \end{bNiceMatrix} \end{equation} % ... 

A starred version of equation environment, that is equation*, typesets everything the same, with one exception that eq. number is not included. It's worth mentioning the shorter notation \[...\] can also be used, which is equivalent of equation* env.

The \quad and \qquad add some space between equations. Otherwise, they would stick together. More precisely, a macro \hspace{<length unit>} will add a specific space, e.g. 1cm, 1mm, 3pt, etc. \quad and \qquad are equivalent of \hspace{1em} and \hspace{2em}, respectively.

With nicematrix.

\documentclass{article} \usepackage{nicematrix} \begin{document} $A = \begin{bNiceMatrix} 0 \\ & 1 & & & & \Block{2-2}<\Huge>{0} \\ & & 0 \\ & & & \frac{1}{2!} \\ & & & & 0 \\ & \Block{2-2}<\Huge>{0} & & & & \frac{1}{3!} \\ & & & & & & \ddots \end{bNiceMatrix}$, $T = \begin{bNiceMatrix} 0 & 1 & \Block[r]{2-2}<\Huge>{0} \\ \Block[l,b]{2-2}<\Huge>{0} & 0 & 1 \\ & & \ddots & \ddots \\ \end{bNiceMatrix} $ \end{document}