Timeline for M-matrix plus S-matrix is P-matrix?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| May 11, 2013 at 16:59 | comment | added | Suvrit | Sorry, i just mistyped the extra word "integral" there...it is of course positive definite over the reals too! | |
| May 10, 2013 at 23:40 | comment | added | Will Sawin | Isn't a symmetric $M$-matrix over the reals positive definite, by one of the standard criteria for positive-definiteness? | |
| May 10, 2013 at 22:53 | comment | added | Suvrit | @Santiago: A symmetric, nonsingular $M$-matrix is a Stieltjes matrix and a symmetric matrix over the integers is Stieltjes if and only if it is positive definite. So at least the integral counterexamples above will not extend to the case when we have symmetry (as the sum of two strictly (symmetric) positive definite matrices cannot lose rank). | |
| May 10, 2013 at 21:05 | comment | added | Santiago | @Will: Thanks for the answer! It is sad to hear that the conjecture is not true. The result is known to be true if $M$ is a diagonal matrix with positive entries. Does the fact that $M$ is highly asymmetric has something to do with it? Could the result we proven if $M$ is a symmetric matrix? I couldn't find any asymmetric counter-example. Thanks again for all your hard work! | |
| May 10, 2013 at 15:45 | vote | accept | Santiago | ||
| May 10, 2013 at 15:45 | history | bounty ended | Santiago | ||
| May 10, 2013 at 6:46 | history | edited | Will Sawin | CC BY-SA 3.0 |
deleted 62 characters in body
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| May 10, 2013 at 6:43 | comment | added | Will Sawin | Oops, that was silly, but your fix certainly works! Or I could admit that the $1$s and the diagonals are really $2$, and turn the $-4$ into a $-32$. | |
| May 10, 2013 at 6:40 | comment | added | Suvrit | (but replacing the 1s by 1/4 and 3/4, in the M and S parts, respectively does the trick) | |
| May 10, 2013 at 6:35 | comment | added | Suvrit | Will, you forgot to add the diagonals! | |
| May 10, 2013 at 5:53 | history | answered | Will Sawin | CC BY-SA 3.0 |