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5 votes
2 answers
2k views

Iterated calculation of determinants

Given a $4 \times 4$ matrix $S$ over a commutative ring $R$. I want to consider it as a $2\times 2$ matrix over $M_2(R)$. Lets say $S=\left(\begin{array}{cc} A&B \\\ C&D\end{array}\right)$ ...
HenrikRüping's user avatar
3 votes
1 answer
628 views

Determinant of block matrix

I expect this to be true and proven, but I can't find any proofs of this. So anyone can confirm or deny this? Let $R$ be a commutative ring, and let $M$ be a $kn\times kn$ matrix, which can be split ...
user105303's user avatar
1 vote
1 answer
227 views

If the direct sum of $L$ and $M$ has a pseudoinverse, then do $L$ and $M$ have pseudoinverses?

Let $L$ and $M$ be matrices over a commutative ring $R$ equipped with an involution "$*$". Define $L \oplus M$ (the "direct sum" of $L$ and $M$) to be $\begin{bmatrix}L & 0 \\ ...
wlad's user avatar
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