Talk:Block matrix

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I have just added the majority of the current page content, so the previous discussions were outdated, since they referred to a considerably different page.Thiagovscoelho (talk) 15:33, 20 March 2024 (UTC)Reply

I believe that the statement "This is also true when ${\displaystyle AB=BA}$, ${\displaystyle AC=CA}$, or ⁠${\displaystyle BD=DB}$⁠." is false.

If ${\displaystyle AC=CA}$, then ${\displaystyle \det {\begin{bmatrix}A&B\\C&D\end{bmatrix}}=\det(AD-CB).}$ Note the change in order of ${\displaystyle C}$ and ${\displaystyle B}$ (we have ${\displaystyle CB}$ instead of ${\displaystyle BC}$). Similarly, if ${\displaystyle BD=DB}$, then ${\displaystyle AD}$ should be replaced with ${\displaystyle DA}$ (i.e. we get ${\displaystyle \det(DA-BC)}$) and if ${\displaystyle AB=BA}$, then we should have ${\displaystyle \det(DA-CB)}$. Note for the last two results, you have to use commutativity of the underlying ring, but not for the first two.

The Surgeon of Death (talk) 14:36, 12 May 2025 (UTC)Reply

I was definitely relying entirely on the sources cited for each of the properties mentioned. Since that sentence did not have a source cited inline next to it, I don't remember why I put that in, if I did, although it may be something I got confused about while reading the sources cited for the surrounding sentences. Thiagovscoelho (talk) 13:09, 9 June 2025 (UTC)Reply