# Betrand

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 Name Betrand Member for 11 months Seen 4 hours ago Website Location Leningrad Age
 May7 comment Literature on Exponential of a Quadratic FormAs 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." May6 comment A spectral radius inequalitysuch that ?? in the first paragraph? Apr19 asked Schur product, partial order Apr9 comment Noncommutative arithmetic mean geometric mean inequality and symmetric polynomialsWhat 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"? Feb6 comment Generalizations of Oppenheim’s inequalityThis would be a big conjecture. I don't know the answer. Would you post it as a new problem. Dec28 comment 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. Dec28 comment Optimization version of the Sylvester equationYou are welcome. Dec27 comment a monotone relation for s-numbers A motivation is from the scalar case, as in this article math.pku.edu.cn/teachers/yaoy/Fall2011/… Dec27 comment a monotone relation for s-numbers What if $A, B$ are positive definite? Dec27 revised When is a Schur complement an $M$-matrix?added 1 characters in body Dec27 comment a monotone relation for s-numbers they are self-ajoint Dec27 asked a monotone relation for s-numbers Dec26 answered Optimization version of the Sylvester equation Dec21 comment Proof of Tracenorm Equality不 客 气。 互 相 帮 忙。^_^ Dec20 accepted Proof of Tracenorm Equality Dec20 revised A curious inequalityedited tags Dec20 revised Proof of Tracenorm Equalityadded 354 characters in body; deleted 1 characters in body Dec20 answered Proof of Tracenorm Equality Dec20 comment Proof of Tracenorm EqualityI think you should have put "the RHS is larger than or equal to the LHS". Dec20 comment 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. Dec7 comment A curious inequalityHere it is. Proposition 8 in Linear Algebra and its Applications 428 (2008) 305–315. Dec7 asked A curious inequality Dec6 comment How to calculate the inverse of the sum of two eigen-decomposed matricesis $x$ given? Are $U, V$ unitary matrices?