# How can I write block matrix like this?

\documentclass{article}

\usepackage{amsmath}

\begin{document}

Thus the matrix representation~$\mathcal{L}$ under the basis is
$\begin{pmatrix} A & & & 0 \\ & A & & \\ & & \ddots & \\ 0 & & & A \end{pmatrix}$
The desired result follows immediately.

\end{document}

• nicematrix is a great extension too!
– NBur
Jan 5 at 8:38

In Plain TeX, your document looks like this:

Thus the matrix representation~$\cal L$ under the basis is
$$\pmatrix{ A & & & 0 \cr & A & & \cr & & \ddots & \cr 0 & & & A }$$
The desired result follows immediately.
\bye