Question

Can $\operatorname{Tr}[A^{-1} BAB^\top]$ be shown to be always positive if $A$ is real and positive definite?

score 50 · Answer 1 · 2026-03-29 18:33:28

50

Views

Can $\operatorname{Tr}[A^{-1} BAB^\top]$ be shown to be always positive if $A$ is real and positive definite?

Published on 29 Mar 2026 - 18:33

score 38 · Answer 2 · 2023-10-01 10:38:20

38

Views

Trace upper bound with commutator

Published on 01 Oct 2023 - 10:38

score 122 · Answer 3 · 2026-02-23 09:00:11

122

Views

Let A be a complex $n \times n$ matrix with rank(A) = 1. Why is the minimal polynomial $x(x-Tr(A))$?

Published on 23 Feb 2026 - 9:00

score 37 · Answer 4 · 2023-10-04 09:59:19

37

Views

Trace of Hermitian involutionary matrix

Published on 04 Oct 2023 - 9:59

score 43 · Answer 5 · 2026-03-26 06:28:36

43

Views

How to calculate the trace of a semigroup?

Published on 26 Mar 2026 - 6:28

score 69 · Answer 6 · 2023-10-08 10:44:41

69

Views

Range of a product of traces

Published on 08 Oct 2023 - 10:44

score 81 · Answer 7 · 2023-10-10 08:43:46

81

Views

Solve for matrix trace equation

Published on 10 Oct 2023 - 8:43

score 107 · Answer 8 · 2026-03-25 23:38:31

107

Views

What is computationally the fastest way to calculate $\mathrm{Tr}(A^n)$ and $\mathrm{Tr}(A^{n-1}B)$?

Published on 25 Mar 2026 - 23:38

score 129 · Answer 9 · 2023-10-21 02:10:59

129

Views

Trace Inequality: prove that for arbitrary square matrix A and B: tr((A+B)(A+B)^T) \leq 2 * tr(AA^T+BB^T)

Published on 21 Oct 2023 - 2:10

score 19 · Answer 10 · 2026-03-26 11:18:21

19

Views

Questions regarding the construction of nilpotent matrices in light of certain characteristics

Published on 26 Mar 2026 - 11:18

score 17 · Answer 11 · 2026-03-13 21:56:34

17

Views

Trace-preserving map between stochastic matrices

Published on 13 Mar 2026 - 21:56

score 82 · Answer 12 · 2023-11-05 10:26:31

82

Views

$Tr[(\vec{n_{1}}\cdot\vec{\sigma})(\vec{n_{2}}\cdot\vec{\sigma})] = \sum_{k,l}(n_1)_{k}(n_{2})_l2\delta_{kl}$

Published on 05 Nov 2023 - 10:26

score 35 · Answer 13 · 2023-11-14 07:15:44

35

Views

How to calculate the square root of a special matrix

Published on 14 Nov 2023 - 7:15

score 47 · Answer 14 · 2026-03-25 18:53:49

47

Views

The covariance matrix $\mathbf{C}$: Why does $\ln \text{det} \mathbf{C}=\text{Tr}\ln \mathbf{C}$ hold?

Published on 25 Mar 2026 - 18:53

score 150 · Answer 15 · 2026-03-26 04:29:00

150

Views

$Tr(A^k) = Tr(B^k)$

Published on 26 Mar 2026 - 4:29

List Question

Can $\operatorname{Tr}[A^{-1} BAB^\top]$ be shown to be always positive if $A$ is real and positive definite?

Trace upper bound with commutator

Let A be a complex $n \times n$ matrix with rank(A) = 1. Why is the minimal polynomial $x(x-Tr(A))$?

Trace of Hermitian involutionary matrix

How to calculate the trace of a semigroup?

Range of a product of traces

Solve for matrix trace equation

What is computationally the fastest way to calculate $\mathrm{Tr}(A^n)$ and $\mathrm{Tr}(A^{n-1}B)$?

Trace Inequality: prove that for arbitrary square matrix A and B: tr((A+B)(A+B)^T) \leq 2 * tr(AA^T+BB^T)

Questions regarding the construction of nilpotent matrices in light of certain characteristics

Trace-preserving map between stochastic matrices

$Tr[(\vec{n_{1}}\cdot\vec{\sigma})(\vec{n_{2}}\cdot\vec{\sigma})] = \sum_{k,l}(n_1)_{k}(n_{2})_l2\delta_{kl}$

How to calculate the square root of a special matrix

The covariance matrix $\mathbf{C}$: Why does $\ln \text{det} \mathbf{C}=\text{Tr}\ln \mathbf{C}$ hold?

$Tr(A^k) = Tr(B^k)$

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