Timeline for Does linearity of cofactor imply linearity of determinant for 3×3 symmetric matrices?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 25, 2022 at 15:49 | answer | added | Robert Bryant | timeline score: 3 | |
| Oct 24, 2022 at 17:30 | comment | added | Iosif Pinelis | @RobertBryant : I see. I did not pay enough attention to the title, which is indeed a bit misleading. However, I find the question interesting and would very much like to see an answer, which is think would be positive! | |
| Oct 24, 2022 at 17:21 | comment | added | Robert Bryant | @IosifPinelis: I agree that that is the literal question, but it seems kind of odd, since the title of the question asks about a property of 'linearity', which is not really relevant if the $a_i$ are not allowed to be variable. | |
| Oct 24, 2022 at 17:05 | comment | added | Iosif Pinelis | @RobertBryant: I think the question is this: If $3\times3$ symmetric matrices $A_i$ and positive reals $a_i$ are such that $\sum_ia_i=1$ and $\cof(\sum_i a_i A_i)=\sum_ia_i\cof A_i$, does it necessarily follow that $\det(\sum_i a_i A_i)=\sum_ia_i\det A_i$? | |
| Oct 24, 2022 at 17:00 | comment | added | Iosif Pinelis | I would certainly like to see to see an answer to this question. So, I don't understand the close votes. Is there an obvious answer? | |
| Oct 24, 2022 at 16:51 | comment | added | Robert Bryant | Just to be clear, are you asking that your matrices $A_i$ $(1\le i\le n)$ be such that for every choice of $a_i>0$ with $a_1+\cdots+a_n=1$, we have $\sum_{i=1}^na_i\,\mathrm{cof}(A_i) =\mathrm{cof}\bigl( \sum_{i=1}^n a_i\,A_i\bigr)$, or just that there is some such choice of $a_i$? | |
| Oct 23, 2022 at 2:26 | review | Close votes | |||
| Nov 2, 2022 at 3:01 | |||||
| Oct 22, 2022 at 20:04 | comment | added | LSpice |
In fact your post was already mostly TeX'd; you just need to wrap TeX in $$. Note the difference between \sigma_i a_i=1 and $\sigma_i a_i=1$ $\sigma_i a_i=1$. But actually please use \sum for sums instead of \sigma (or rather \Sigma, which is what you probably meant); compare, for example, $\Sigma_i a_i=1$ \Sigma_i a_i=1 to $\sum_i a_i=1$ \sum_i a_i=1, and especially $\displaystyle\Sigma_i a_i=1$ \displaystyle\Sigma_i a_i=1 to $\displaystyle\sum_i a_i=1$ \displaystyle\sum_i a_i=1. I have edited accordingly.
|
|
| Oct 22, 2022 at 20:03 | history | edited | LSpice | CC BY-SA 4.0 |
TeX
|
| Oct 22, 2022 at 19:05 | comment | added | Glorfindel | Welcome to MathOverflow! You can improve the formatting of your post by editing it to use MathJax; see this link for a tutorial. | |
| S Oct 22, 2022 at 19:03 | review | First questions | |||
| Oct 22, 2022 at 19:05 | |||||
| S Oct 22, 2022 at 19:03 | history | asked | Yacine | CC BY-SA 4.0 |