Timeline for Rank changes with matrix edits
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Jul 16, 2022 at 9:11 | history | edited | Felix Goldberg | CC BY-SA 4.0 |
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| Feb 3, 2015 at 13:42 | comment | added | Turbo | can you update your answer? So that I could close. | |
| Feb 3, 2015 at 13:42 | comment | added | Felix Goldberg | @Turbo Yes, I think it does. | |
| Feb 3, 2015 at 12:38 | comment | added | Turbo | So you say in this case $rank(M\pm W)\in[rank(M)-2,rank(M)+2]$? | |
| Feb 3, 2015 at 7:03 | comment | added | Turbo | Problem reduces to rank $2$ in symmetric case. | |
| Feb 3, 2015 at 6:39 | comment | added | Felix Goldberg | @Turbo In that case, things are open again.... :( If you want to discuss the specific case, feel free to email me. | |
| Feb 3, 2015 at 6:37 | comment | added | Felix Goldberg | @Turbo Yes, all you need is Hermitianness of $M$ and $W$. But as I said, having $\{0,1\}$ helps to perhaps pinpoint precisely which of the three cases occurs. | |
| Feb 3, 2015 at 6:36 | comment | added | Felix Goldberg | @Turbo The magic works because it's a rank 1 update. It's possible to use interlacing for rank $k$ updates, but the bounds get progressively weaker, of course. The proof for rank $k$ is just an inductive application of Corollary 4.3.9 $k$ times (decompose $W$ as the sum of $k$ matrices of rank $1$). | |
| Feb 3, 2015 at 6:34 | comment | added | Felix Goldberg | @Turbo It's proved in the reference I gave (the standard one on the subject). | |
| Feb 3, 2015 at 6:32 | history | answered | Felix Goldberg | CC BY-SA 3.0 |