Talk:Block matrix

Major revision, archived previous talk page

I have just added the majority of the current page content, so the previous discussions were outdated, since they referred to a considerably different page.Thiagovscoelho (talk) 15:33, 20 March 2024 (UTC)

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

If $AC=CA$, then $\det {\begin{bmatrix}A&B\\C&D\end{bmatrix}}=\det(AD-CB).$ Note the change in order of $C$ and $B$ (we have $CB$ instead of $BC$). Similarly, if $BD=DB$, then $AD$ should be replaced with $DA$ (i.e. we get $\det(DA-BC)$) and if $AB=BA$, then we should have $\det(DA-CB)$. 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)