Betrand
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Registered User
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May 7 |
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Literature on Exponential of a Quadratic Form As each summand is concave, so f is concave. A relevant problem is when a product of quadratic form is convex. A reference comes to me is the paper "Lin, Sinnamon, A condition for convexity of a product of positive definite quadratic forms, SIAM J. Matrix Anal. Appl. 32 (2011) 457-462." |
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May 6 |
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A spectral radius inequality such that ?? in the first paragraph? |
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Apr 19 |
asked | Schur product, partial order |
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Apr 9 |
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Noncommutative arithmetic mean geometric mean inequality and symmetric polynomials What do you mean by "The two matrix version of the my conjecture follows immediately from a stronger conjecture of Bhatia and Kittaneh that was actually recently resolved"? |
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Feb 6 |
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Generalizations of Oppenheim’s inequality This would be a big conjecture. I don't know the answer. Would you post it as a new problem. |
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Dec 28 |
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a monotone relation for s-numbers Thanks, but how do you define determinant? If $A, B$ are positive definite matrices, we have $|\det(2A+iB)|\ge |\det(A+iB)|$; see Lemma 5 of Kh. D. Ikramov, Determinantal inequalities for accretive-dissipative matrices, J. Math. Sci. (N. Y.), 121(2004) 2458-2464. |
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Dec 28 |
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Optimization version of the Sylvester equation You are welcome. |
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Dec 27 |
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a monotone relation for s-numbers A motivation is from the scalar case, as in this article math.pku.edu.cn/teachers/yaoy/Fall2011/… |
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Dec 27 |
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a monotone relation for s-numbers What if $A, B$ are positive definite? |
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Dec 27 |
revised |
When is a Schur complement an $M$-matrix? added 1 characters in body |
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Dec 27 |
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a monotone relation for s-numbers they are self-ajoint |
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Dec 27 |
asked | a monotone relation for s-numbers |
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Dec 26 |
answered | Optimization version of the Sylvester equation |
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Dec 21 |
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Proof of Tracenorm Equality 不 客 气。 互 相 帮 忙。^_^ |
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Dec 20 |
accepted | Proof of Tracenorm Equality |
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Dec 20 |
revised |
A curious inequality edited tags |
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Dec 20 |
revised |
Proof of Tracenorm Equality added 354 characters in body; deleted 1 characters in body |
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Dec 20 |
answered | Proof of Tracenorm Equality |
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Dec 20 |
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Proof of Tracenorm Equality I think you should have put "the RHS is larger than or equal to the LHS". |
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Dec 20 |
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is there any relationship between the eigenvector of sum(AA'+BB') and sum(A’A+B’B) ? I guess $A′$ means the transpose. Steven shows the eigenvectors are generally different. However, there is an interesting relation between the eigenvalues, under a mild assumption. See Corollary 2.2. of Lin & Wolkowicz, An eigenvalue majorization inequality for positive semidefinite block matrices, Linear Multilinear Algebra, 60 (2012), 1365-1368. |
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Dec 7 |
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A curious inequality Here it is. Proposition 8 in Linear Algebra and its Applications 428 (2008) 305–315. |
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Dec 7 |
asked | A curious inequality |
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Dec 6 |
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How to calculate the inverse of the sum of two eigen-decomposed matrices is $x$ given? Are $U, V$ unitary matrices? |
