Let matrix $M$ be \begin{align*} M= \begin{pmatrix} A_1 & 0 & 0 & \cdots & 0 \\ 0 & A_2 & 0 & \cdots & 0 \\ \vdots \\ 0 & 0 & 0 & \cdots & A_n \end{pmatrix} \end{align*} where $A_1, A_2, ..., A_n$ are rectangular matrices (could be of different types). What is the formula of calculating determinant of such matrix?
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2If the blocks are of square size, then $\det(M)=\prod_i \det(A_i)$. Otherwise there is no easy formula. – Dietrich Burde May 08 '21 at 12:00
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3In case when $A_i$ are not square matrices the determinant seems to be equal $0$. ( linear dependence of some columns or rows) – Widawensen May 08 '21 at 14:01
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2That is so neat @Widawensen that you should post it as an answer. – ancient mathematician May 08 '21 at 14:09