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What is the English term for "cellular triangular matrix " i.e. a matrix like e.g.

$$ \begin{bmatrix} 1 & 2& 4 & & & & & \\ 2 & 3& 5 & & & & & \\ 7 & 8& 1 & & & & & \\ &&&7&&&&\\ &&&&4&5&&\\ &&&&2&1&&\\ &&&&&&8&9\\ &&&&&&2&6 \end{bmatrix} $$

All the other elements are zeros.

What happens when we raise it to some power n? I think effectively the smaller matrices along the main diagonal are raised to power n.

I need the English term so that I can look up some more information about these matrices and their properties.

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    $\begingroup$ I would call this "block diagonal." $\endgroup$
    – Sean Roberson
    Commented Jun 18, 2022 at 21:43
  • $\begingroup$ Here is the link to wiki. $\endgroup$
    – WhatsUp
    Commented Jun 18, 2022 at 21:46
  • $\begingroup$ Thank you both! $\endgroup$
    – peter.petrov
    Commented Jun 18, 2022 at 21:49
  • $\begingroup$ If you answer a question in a comment, it goes into the list of unanswered questions. This site already has over 300,000 unanswered questions, so there is a good reason to answer questions in the answer box. $\endgroup$
    – Suzu Hirose
    Commented Jun 18, 2022 at 22:52

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These matrices are called block diagonal matrices.

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  • $\begingroup$ Thanks. What happens when we raise it to some power $n$? Each of the blocks "along the main diagonal" gets raised to power $n$, right? Are there any other special properties of these matrices? $\endgroup$
    – peter.petrov
    Commented Jun 20, 2022 at 9:06

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