Timeline for If $S$ is a nonsingular symmetric matrix over a number field and $D_k$ is its principal minor of order $k$, is $\frac{D_k}{D_{k-1}} > 0$ always true?
Current License: CC BY-SA 4.0
29 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 13, 2018 at 20:00 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Oct 14, 2018 at 19:40 | answer | added | Federico Poloni | timeline score: 1 | |
| Oct 14, 2018 at 19:00 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Sep 14, 2018 at 18:01 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Aug 15, 2018 at 17:23 | history | edited | David Handelman | CC BY-SA 4.0 |
non is NOT a word (in English)
|
| Aug 15, 2018 at 17:00 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jul 16, 2018 at 16:39 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jun 16, 2018 at 16:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| May 17, 2018 at 15:15 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Apr 17, 2018 at 15:10 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Mar 18, 2018 at 14:29 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Feb 16, 2018 at 13:43 | history | edited | Abdu Magdy | CC BY-SA 3.0 |
corrected some typos.
|
| Feb 16, 2018 at 13:24 | history | edited | Abdu Magdy | CC BY-SA 3.0 |
corrected some typos.
|
| Feb 16, 2018 at 12:59 | comment | added | Abdu Magdy | Dear @Peter Heinig, Thank you so much :) | |
| Feb 16, 2018 at 9:08 | comment | added | Peter Heinig | Dear @ Abdu Magdy: I added the theorem that the statement you are asking about is a corollary of. Speaking to the content to your question: while I did not look long into Gantmacher's book, as far as I can see you have a point, in that while Theorem 3 ensures that $D_k D_{k-1}$ is nonzero, there does not seem to be any condition ensuring that it is $>0$. | |
| Feb 16, 2018 at 9:06 | history | edited | Peter Heinig | CC BY-SA 3.0 |
Added the full reference to the book the OP is asking about. Added the theorem that the statement the OP is asking about is a corollary of.
|
| Feb 14, 2018 at 18:39 | vote | accept | Abdu Magdy | ||
| Feb 14, 2018 at 18:40 | |||||
| Feb 12, 2018 at 20:38 | answer | added | Abdu Magdy | timeline score: 0 | |
| Feb 12, 2018 at 18:57 | comment | added | Abdu Magdy | @PeterHeinig But if $F=R$, there is no square root of negative numbers. Hence $D_kD_{k-1}$ must be greater than $0$. Am I missing something? | |
| Feb 12, 2018 at 18:52 | comment | added | Abdu Magdy | @PeterHeinig I've done that because while pondering on the corollary I realized that for the corollary to be true $$b_{kk}= \pm \sqrt{\frac{D_k}{D_{k-1}}} $$ must be true (Implied from the related theorem in the same book). So, I had two versions of the same question. | |
| Feb 12, 2018 at 18:46 | comment | added | Abdu Magdy | @AbdelmalekAbdesselam There is no such hypothesis. My reputations prevented me from uploading a picture of the whole theorem. But it's a theorem about decomposing a matrix into triangular factors. | |
| Feb 12, 2018 at 18:45 | comment | added | Peter Heinig | @AbduMagdy: their signs are the same; it is irritating all the same that the title does not agree with the OP. | |
| Feb 12, 2018 at 18:42 | comment | added | Abdelmalek Abdesselam | there is probably a missing hypothesis here like the matrix is positive definite. | |
| Feb 12, 2018 at 18:42 | comment | added | Abdu Magdy | @PeterHeinig They're pretty much the same. Either one implies the other. | |
| Feb 12, 2018 at 18:41 | comment | added | Abdu Magdy | @AbdelmalekAbdesselam Then, is the corollary wrong? | |
| Feb 12, 2018 at 18:41 | comment | added | Peter Heinig | @Abdu Magdy: the $\frac{D_k}{D_{k-1}}$ does not agree with the $D_kD_{k-1}$ in the OP. | |
| Feb 12, 2018 at 18:39 | comment | added | Abdelmalek Abdesselam | no. just take a diagonal matrix. | |
| Feb 12, 2018 at 18:25 | review | First posts | |||
| Feb 12, 2018 at 18:43 | |||||
| Feb 12, 2018 at 18:21 | history | asked | Abdu Magdy | CC BY-SA 3.0 |