Timeline for What are good bounds on ratios of subdeterminants?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Mar 16, 2015 at 11:02 | comment | added | user35593 | By some transformations $$\frac{\det(A_i)}{\det(A)}=\frac{1}{a_{ii}-v^TA_i^{-1}v}$$ where $v$ is the $i$-th row of $A$ without $a_{ii}$. | |
| Mar 13, 2015 at 22:26 | comment | added | user6818 | Could you kindly elaborate? | |
| Mar 13, 2015 at 22:09 | comment | added | Suvrit | You can also use convexity of this function to get some bounds. | |
| Mar 13, 2015 at 21:24 | comment | added | Igor Rivin | @AlexDegtyarev Simpler put: take a diagonal matrix. | |
| Mar 13, 2015 at 20:43 | comment | added | Alex Degtyarev | Clearly, both bounds are sharp: take for $A$ a matrix whose minimal or maximal eigenvalue equals $1$ and the corresponding eigenspace splits off as an orthogonal summand. (I mean, is a coordinate line.) | |
| Mar 13, 2015 at 20:18 | comment | added | The Masked Avenger | You should assume A is nonsingular. Also, inspired by the idea of looking at a related ratio of the area of a face of a parallelipiped to its volume, I doubt that much more can be said. | |
| Mar 13, 2015 at 20:12 | history | asked | user6818 | CC BY-SA 3.0 |