To be specific, I want to set the following matrix: 
I already read Draw a box around matrix elements, but I dont know, how one makes a block "T" of this size.
How do I do this?
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2 Answers
A normal pmatrix from amsmath can serve what you want. To construct that "T block", just use \boxed{~T~}. The tildes ~ are there to make the T wider, and you can also add the superscript 1 by doing \makebox[0pt]{$^1~~$} to cancel its width.
Finally, observe that \setlength\arraycolsep{0pt} for removing spacing between columns only for this matrix.
\documentclass{article} \usepackage{amsmath} \begin{document} \newcommand{\tblk}{\makebox[0pt]{$^1~~$}\boxed{~T~}} \[ \setlength\arraycolsep{0pt} A = \begin{pmatrix} \boxed{~T~} & & & \\ & \tblk & & \\ & & \ddots & \\ & & & \tblk \end{pmatrix} \] \end{document} 
Since you tag this tikz-matrix, I use one of these. There it is pretty straightforward to put nodes with any desired property.
\documentclass{article} \usepackage{tikz} \usetikzlibrary{matrix,positioning} \begin{document} \[ A=\vcenter{\hbox{ \begin{tikzpicture}[T-block/.style={draw,minimum width=12mm,minimum height=5mm}] \matrix (m)[matrix of math nodes,nodes in empty cells, left delimiter=(,right delimiter=)] { |[T-block]| T & & & \\ & |[T-block]| T & & \\ & & |[T-block,draw=none]|& \\ & & & |[T-block]| T \\ } ; \draw[dotted,thick] (m-2-2) -- (m-4-4); \node[left=0pt of m-2-2.north west,anchor=north east,inner sep=1pt, font=\small] {1}; \node[left=0pt of m-4-4.north west,anchor=north east,inner sep=1pt, font=\small] {1}; \end{tikzpicture}}} \] \end{document} 