Timeline for On a determinant inequality of positive definite matrices
Current License: CC BY-SA 3.0
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| Sep 26, 2013 at 16:15 | comment | added | Suvrit | Even with the all diagonal elements equal this does not hold; take the matrix $B$ that I have above, set its diagonal to 15 (it still remains posdef); the conjecture still fails. Perhaps for it to hold $C$ has to depend on $n$ (the size of the matrices)---but am not sure about that. You might want to pose it as a separate problem. | |
| Sep 26, 2013 at 10:45 | comment | added | Arash | Many thanks for the answer. Unfortunately I forgot to write an important assumption about $B$. All diagonal elements are equal: $b_{11}=...=b_{nn}=K$. I am not sure if this is significant or not for the problem. As a matter of fact I was trying to find an upper bound like $C\det(I+AB^*)\geq \det(I+AB)$ for some $C$ independent of the dimension of $B$. I wonder if this is possible. My numerical evaluation of the current problem shows that with this additional assumption, we can have $C=2$. I might have mistaken somewhere. Should I post this as question, if it can be an independent problem? | |
| Sep 26, 2013 at 10:38 | vote | accept | Arash | ||
| Sep 26, 2013 at 0:36 | history | answered | Suvrit | CC BY-SA 3.0 |