Question

Could we find a constant $a$ such that $\operatorname{Tr}(M^{\top}N + N^{\top}M) \ge a \operatorname{Tr}(M^{\top}M)$?

score 44 · Answer 1 · 2026-04-17 12:10:37

44

Views

Could we find a constant $a$ such that $\operatorname{Tr}(M^{\top}N + N^{\top}M) \ge a \operatorname{Tr}(M^{\top}M)$?

Published on 17 Apr 2026 - 12:10

score 102 · Answer 2 · 2026-04-09 21:25:27

102

Views

Norm of a 2-by-2 matrix

Published on 09 Apr 2026 - 21:25

score 893 · Answer 3 · 2026-05-10 16:57:10

893

Views

Spectral radius is the greatest lower bound for some matrix norm

Published on 10 May 2026 - 16:57

score 47 · Answer 4 · 2026-04-10 21:21:04

47

Views

Derive a Matrix from Vectors

Published on 10 Apr 2026 - 21:21

score 96 · Answer 5 · 2026-03-25 11:16:33

96

Views

Is it possible to define a scalar valued function $f$ over positive definite matrices, such that $f(X) \le f(Y)$ implies $X \preceq Y$?

Published on 25 Mar 2026 - 11:16

score 49 · Answer 6 · 2026-04-17 03:08:43

49

Views

Upper bound on the trace of k-th Frechet derivative of the matrix function $|x^k|$

Published on 17 Apr 2026 - 3:08

score 306 · Answer 7 · 2026-05-10 13:48:55

306

Views

using Schur's complement and Young's inequality to reduce matrix algebraic equation to LMI

Published on 10 May 2026 - 13:48

score 166 · Answer 8 · 2026-04-11 15:32:14

Is it possible to lower bound ${\bf tr}(XYZ)$ in terms of $X, Y, Z$ provided that $X, Y, Z$ are all symmetric and positive definite?

score 126 · Answer 9 · 2026-04-16 03:50:33

126

Views

Is $X-BXB$ positive definite provided $X, B$ are both symmetric and positive definite?

Published on 16 Apr 2026 - 3:50

score 207 · Answer 10 · 2026-04-16 17:16:24

207

Views

Estimate parameter $a$ such that $tr \left[ A (B- (I-aC)B(I-aC) ) \right] > 0$.

Published on 16 Apr 2026 - 17:16

score 52 · Answer 11 · 2026-04-11 21:18:38

52

Views

Diophantine matrix equation - Solver or algorithm

Published on 11 Apr 2026 - 21:18

score 74 · Answer 12 · 2026-04-16 13:39:38

74

Views

Lower bound ${\bf tr}(XY) - {\bf tr}(XZY)$ by ${\bf tr}(X)$ provided $X, Y, Z$ all real symmetric

Published on 16 Apr 2026 - 13:39

score 267 · Answer 13 · 2026-04-14 04:41:50

267

Views

Is it possbile to upper bound ${\bf tr}(ABC)$ by ${\bf tr}(AB)$ provided $A,B,C$ are all real, symmetric and positive definite?

Published on 14 Apr 2026 - 4:41

score 155 · Answer 14 · 2026-04-13 23:54:11

155

Views

Singular value of matrices whose entries are on the unit circle

Published on 13 Apr 2026 - 23:54

score 531 · Answer 15 · 2026-04-16 13:37:17

531

Views

Second order Taylor expansion of Frobenius norm

Published on 16 Apr 2026 - 13:37

List Question

Could we find a constant $a$ such that $\operatorname{Tr}(M^{\top}N + N^{\top}M) \ge a \operatorname{Tr}(M^{\top}M)$?

Norm of a 2-by-2 matrix

Spectral radius is the greatest lower bound for some matrix norm

Derive a Matrix from Vectors

Is it possible to define a scalar valued function $f$ over positive definite matrices, such that $f(X) \le f(Y)$ implies $X \preceq Y$?

Upper bound on the trace of k-th Frechet derivative of the matrix function $|x^k|$

using Schur's complement and Young's inequality to reduce matrix algebraic equation to LMI

Is it possible to lower bound ${\bf tr}(XYZ)$ in terms of $X, Y, Z$ provided that $X, Y, Z$ are all symmetric and positive definite?

Is $X-BXB$ positive definite provided $X, B$ are both symmetric and positive definite?

Estimate parameter $a$ such that $tr \left[ A (B- (I-aC)B(I-aC) ) \right] > 0$.

Diophantine matrix equation - Solver or algorithm

Lower bound ${\bf tr}(XY) - {\bf tr}(XZY)$ by ${\bf tr}(X)$ provided $X, Y, Z$ all real symmetric

Is it possbile to upper bound ${\bf tr}(ABC)$ by ${\bf tr}(AB)$ provided $A,B,C$ are all real, symmetric and positive definite?

Singular value of matrices whose entries are on the unit circle

Second order Taylor expansion of Frobenius norm

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