Talk:Block matrix

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To-do list for Block matrix: edit · history · watch · refresh · Updated 2007-11-28 Add general formula for the determinant for ${\displaystyle {\begin{pmatrix}A&B\\C&D\end{pmatrix}}}$

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Major revision, archived previous talk page

Latest comment: 2 months ago3 comments2 people in discussion

I have just added the majority of the current page content, so the previous discussions were outdated, since they referred to a considerably different page.Thiagovscoelho (talk) 15:33, 20 March 2024 (UTC)Reply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