Timeline for Factoring positive semidefinite matrices over $\mathbb{Q}[i]$
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 2, 2023 at 1:31 | history | edited | LSpice | CC BY-SA 4.0 |
Capitalise title
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| Feb 27, 2023 at 16:41 | answer | added | Bewol | timeline score: 3 | |
| S Feb 22, 2023 at 19:17 | history | suggested | CommunityBot | CC BY-SA 4.0 |
expanded acronym "psd" in title
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| Feb 22, 2023 at 18:35 | review | Suggested edits | |||
| S Feb 22, 2023 at 19:17 | |||||
| Feb 22, 2023 at 17:44 | history | edited | Dima Pasechnik | CC BY-SA 4.0 |
added example and a better question
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| Feb 22, 2023 at 14:43 | history | edited | Dima Pasechnik | CC BY-SA 4.0 |
added extra condition
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| Feb 22, 2023 at 14:25 | comment | added | Dima Pasechnik | @ChrisWuthrich - your example is not psd | |
| Feb 22, 2023 at 14:23 | comment | added | Dima Pasechnik | sorry, edited the question so that it makes sense, indeed, the condition on $\det P$ is needed. | |
| Feb 22, 2023 at 14:16 | comment | added | Chris Wuthrich | .. and how do you diagonalise $(\begin{smallmatrix} 0 & 2\\1& 0 \end{smallmatrix})$ staying over $\mathbb{Q}$? | |
| Feb 22, 2023 at 14:04 | comment | added | YCor | @DimaPasechnik but $\det(P)^{1/n}$ is not necessary in $\mathbf{Q}$... | |
| Feb 22, 2023 at 14:02 | comment | added | Dima Pasechnik | $P$ is p.s.d., its determinant is in $\mathbb{Q}$, anyway | |
| Feb 22, 2023 at 14:01 | comment | added | YCor | @DimaPasechnik Tom's point is that the possibility writing the matrix in this way implies that $\det(P)^{1/n}$ belongs to $\mathbf{Q}[i]$. And this is not always true (take $n\ge 2$ and $P$ be diagonal($2,1,\dots,1$)). | |
| Feb 22, 2023 at 13:58 | comment | added | Dima Pasechnik | no, why? The $1/n$ is there cause for a scalar $t$ one has $\det (tI)=t^n$, and I'd like $\det P$ to cancel each other on both sides of $P=tAA^*$. | |
| Feb 22, 2023 at 13:53 | comment | added | Tom De Medts | Do you assume $\det P$ to be an $n$-th power of a rational number? | |
| Feb 22, 2023 at 13:53 | answer | added | marco | timeline score: 1 | |
| Feb 22, 2023 at 13:19 | history | asked | Dima Pasechnik | CC BY-SA 4.0 |