Question

If $(\cdots A_{i_3}A_{i_2}A_{i_1})x_0\to 0$ for some $x_0$, what happens for any other $x$?

score 20 · Answer 1 · 2021-07-27 09:26:43

20

Views

If $(\cdots A_{i_3}A_{i_2}A_{i_1})x_0\to 0$ for some $x_0$, what happens for any other $x$?

Published on 27 Jul 2021 - 9:26

score 91 · Answer 2 · 2021-08-03 15:28:25

91

Views

Matrix Reconstruction from Products

Published on 03 Aug 2021 - 15:28

score 156 · Answer 3 · 2021-08-13 07:49:38

156

Views

The trace property of product of positive operators $\text{Tr}(ABBA)^\alpha = \text{Tr}(BAAB)^\alpha$?

Published on 13 Aug 2021 - 7:49

score 84 · Answer 4 · 2021-08-21 06:28:25

84

Views

How to prove that $\|\Sigma-\mu I\|^2+E\left[\|S-\Sigma\|^2\right] = E\|S-\mu I\|^{2}$?

Published on 21 Aug 2021 - 6:28

score 88 · Answer 5 · 2021-08-27 21:21:14

88

Views

Prove that $A \mapsto A (A + \lambda)^{-1}$ is Frechet differentiable for any positive matrix $A$ and for any $\lambda \gt 0.$

Published on 27 Aug 2021 - 21:21

score 48 · Answer 6 · 2021-08-28 09:20:33

48

Views

Multiplying a matrix by a certain unitary matrix: effect on the eigenvalues

Published on 28 Aug 2021 - 9:20

score 54 · Answer 7 · 2021-08-29 12:03:57

54

Views

Proving that $\varphi$ is operator convex.

Published on 29 Aug 2021 - 12:03

score 267 · Answer 8 · 2021-08-29 14:42:06

267

Views

Proving an inequality for operators.

Published on 29 Aug 2021 - 14:42

score 111 · Answer 9 · 2021-09-01 06:53:24

111

Views

Product of unitary matrix and hermitian matrix

Published on 01 Sep 2021 - 6:53

score 67 · Answer 10 · 2021-09-25 11:36:34

67

Views

Minimax type principle for a self-adjoint operator acting on a Hilbert space

Published on 25 Sep 2021 - 11:36

score 62 · Answer 11 · 2021-10-29 06:19:29

62

Views

Bound of weighted trace of a self-adjoint matrix

Published on 29 Oct 2021 - 6:19

score 152 · Answer 12 · 2021-11-11 12:21:16

152

Views

Matrix logarithm of unitary matrix from polar decomposition of product of positive definite matrices

Published on 11 Nov 2021 - 12:21

score 122 · Answer 13 · 2021-11-19 13:57:26

122

Views

Matrix logarithm of unitary matrix from eigendecomposition of Hermitian matrix

Published on 19 Nov 2021 - 13:57

score 61 · Answer 14 · 2021-11-24 19:27:19

61

Views

What is the solution to this matrix optimization problem $A^* = \text{argmin}_{A} \sum_{i=1}^{r-1}|Ax_i-x_{i+1}|^2$?

Published on 24 Nov 2021 - 19:27

score 73 · Answer 15 · 2021-12-15 06:17:35

73

Views

How to prove spectral radius of $A-A^{\infty}$ is less than 1? $A$ is semi convergent

Published on 15 Dec 2021 - 6:17

List Question

If $(\cdots A_{i_3}A_{i_2}A_{i_1})x_0\to 0$ for some $x_0$, what happens for any other $x$?

Matrix Reconstruction from Products

The trace property of product of positive operators $\text{Tr}(ABBA)^\alpha = \text{Tr}(BAAB)^\alpha$?

How to prove that $\|\Sigma-\mu I\|^2+E\left[\|S-\Sigma\|^2\right] = E\|S-\mu I\|^{2}$?

Prove that $A \mapsto A (A + \lambda)^{-1}$ is Frechet differentiable for any positive matrix $A$ and for any $\lambda \gt 0.$

Multiplying a matrix by a certain unitary matrix: effect on the eigenvalues

Proving that $\varphi$ is operator convex.

Proving an inequality for operators.

Product of unitary matrix and hermitian matrix

Minimax type principle for a self-adjoint operator acting on a Hilbert space

Bound of weighted trace of a self-adjoint matrix

Matrix logarithm of unitary matrix from polar decomposition of product of positive definite matrices

Matrix logarithm of unitary matrix from eigendecomposition of Hermitian matrix

What is the solution to this matrix optimization problem $A^* = \text{argmin}_{A} \sum_{i=1}^{r-1}|Ax_i-x_{i+1}|^2$?

How to prove spectral radius of $A-A^{\infty}$ is less than 1? $A$ is semi convergent

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