Timeline for Which matrix decompositions feature permutation matrices?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Jan 19, 2021 at 11:40 | comment | added | Andrei Smolensky | I would say that LU and LUP decompositions are somewhat distinct from Bruhat decomposition for they work for singular matrices as well. | |
| Jan 19, 2021 at 2:59 | comment | added | David E Speyer | You may be right. | |
| Jan 19, 2021 at 2:30 | comment | added | LSpice | @DavidESpeyer, I thought that the term "LU decomposition" was often used even when there was a permutation involved, as in the Wikipedia article, thus allowing it to recover the whole Bruhat decomposition. I agree that, if one restricts to the literal name, then one only recovers (a translate of) the big cell. | |
| Jan 19, 2021 at 2:14 | comment | added | David E Speyer | In various contexts, people will say that Bruhat decomposition is $\bigsqcup LwL$, $\bigsqcup LwU$, $\bigsqcup UwL$ or $\bigsqcup UwU$. This issue doesn't affect the point I am making. | |
| Jan 19, 2021 at 2:13 | comment | added | David E Speyer | @LSpice I would say that LU decomposition is the largest piece of Bruhat decomposition. That it to say, Bruhat decomposition is $GL_n = \bigsqcup_{w \in S_n} L w U$. The $LU$ decomposition is the observation that the $w = \mathrm{Id}$ piece covers all but a piece of measure $0$. | |
| Jan 19, 2021 at 0:10 | comment | added | LSpice | @FrancoisZiegler, isn't the LU decomposition just a translate of the Bruhat decomposition for $\operatorname{GL}_n$? | |
| Jan 18, 2021 at 23:53 | comment | added | wlad | @FrancoisZiegler That's a good one, thanks | |
| Jan 18, 2021 at 23:45 | comment | added | Francois Ziegler | en.wikipedia.org/wiki/Bruhat_decomposition | |
| Jan 18, 2021 at 23:41 | history | edited | wlad | CC BY-SA 4.0 |
added 2 characters in body
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| Jan 18, 2021 at 23:40 | history | undeleted | wlad | ||
| Jan 18, 2021 at 23:06 | history | deleted | wlad | via Vote | |
| Jan 18, 2021 at 23:01 | comment | added | wlad | Question author here: It looks like the RRQR decomposition is an example | |
| Jan 18, 2021 at 23:00 | history | asked | wlad | CC BY-SA 4.0 |