Question

Prove $||A||_{2,\infty} = \max_{1\le i \le m}\sqrt{\sum_{j=1}^{n} |a_{ij}|^{2}}$

score 103 · Answer 1 · 2020-08-16 05:56:53

103

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Prove $||A||_{2,\infty} = \max_{1\le i \le m}\sqrt{\sum_{j=1}^{n} |a_{ij}|^{2}}$

Published on 16 Aug 2020 - 5:56

score 710 · Answer 2 · 2026-03-26 12:37:14

710

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An inequality about the Frobenius norm of the difference of two Hermitian matrices

Published on 26 Mar 2026 - 12:37

score 242 · Answer 3 · 2020-08-23 18:40:51

242

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Bounds for the quadratic form of inverse block matrix

Published on 23 Aug 2020 - 18:40

score 157 · Answer 4 · 2020-08-25 16:59:59

157

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Prove bound on matrix norms

Published on 25 Aug 2020 - 16:59

score 146 · Answer 5 · 2026-03-25 11:16:30

146

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How to compare the nuclear seminorm of a matrix with the nuclear norm of the same matrix?

Published on 25 Mar 2026 - 11:16

score 57 · Answer 6 · 2020-09-02 16:05:57

57

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How to prove that the weighted $l_1$ norm enhance the sparsity more than the traditional $l_1$norm

Published on 02 Sep 2020 - 16:05

score 1.4k · Answer 7 · 2020-09-05 03:11:54

1.4k

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How to prove the following matrix inequalities: $ \|A\|_1\leq\sqrt{n}\|A\|_2\leq n\|A\|_1$ and $\|A\|_\infty\leq\sqrt{n}\|A\|_2\leq n\|A\|_{\infty}$

Published on 05 Sep 2020 - 3:11

score 84 · Answer 8 · 2020-09-14 20:48:33

84

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$\| \mathbf{A} \|_1 \ne \sum_{i = 1}^{M} \sum_{j = 1}^{N} |a_{i,j}|$?

Published on 14 Sep 2020 - 20:48

score 109 · Answer 9 · 2026-03-25 16:13:51

109

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Let $A$ be symmetric and positive definite. Suppose $A=LL^T$ is its Cholesky decomposition. Prove that $||A||_2=||L||_2^2$.

Published on 25 Mar 2026 - 16:13

score 448 · Answer 10 · 2020-10-07 04:14:36

448

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Is the matrix norm $\mu(A)=n\max_{i,j}|a_{ij}|$ for $A\in\mathbb R^{n\times n}$ NOT compatible with any vector norm on $\mathbb R^n$?

Published on 07 Oct 2020 - 4:14

score 58 · Answer 11 · 2020-10-12 18:10:32

58

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Is there a condition for $\| T\| =\| T^\ast\|$ where $T$ is a linear operator.

Published on 12 Oct 2020 - 18:10

score 550 · Answer 12 · 2020-10-15 13:44:03

550

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Differentiation of Matrix Norm

Published on 15 Oct 2020 - 13:44

score 195 · Answer 13 · 2020-10-15 15:00:46

195

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On the norm of a quadratic form associated with a matrix product

Published on 15 Oct 2020 - 15:00

score 506 · Answer 14 · 2020-10-20 10:20:34

506

Views

Product Inequality for Schatten p-norm of Matrices

Published on 20 Oct 2020 - 10:20

score 41 · Answer 15 · 2020-10-23 12:20:42

41

Views

Algorithm for Generalized Singular Vectors: $\text{argsup}_{\|x\|_p=\|y\|_q=1} x^T A y$

Published on 23 Oct 2020 - 12:20

List Question

Prove $||A||_{2,\infty} = \max_{1\le i \le m}\sqrt{\sum_{j=1}^{n} |a_{ij}|^{2}}$

An inequality about the Frobenius norm of the difference of two Hermitian matrices

Bounds for the quadratic form of inverse block matrix

Prove bound on matrix norms

How to compare the nuclear seminorm of a matrix with the nuclear norm of the same matrix?

How to prove that the weighted $l_1$ norm enhance the sparsity more than the traditional $l_1$norm

How to prove the following matrix inequalities: $ \|A\|_1\leq\sqrt{n}\|A\|_2\leq n\|A\|_1$ and $\|A\|_\infty\leq\sqrt{n}\|A\|_2\leq n\|A\|_{\infty}$

$\| \mathbf{A} \|_1 \ne \sum_{i = 1}^{M} \sum_{j = 1}^{N} |a_{i,j}|$?

Let $A$ be symmetric and positive definite. Suppose $A=LL^T$ is its Cholesky decomposition. Prove that $||A||_2=||L||_2^2$.

Is the matrix norm $\mu(A)=n\max_{i,j}|a_{ij}|$ for $A\in\mathbb R^{n\times n}$ NOT compatible with any vector norm on $\mathbb R^n$?

Is there a condition for $\| T\| =\| T^\ast\|$ where $T$ is a linear operator.

Differentiation of Matrix Norm

On the norm of a quadratic form associated with a matrix product

Product Inequality for Schatten p-norm of Matrices

Algorithm for Generalized Singular Vectors: $\text{argsup}_{\|x\|_p=\|y\|_q=1} x^T A y$

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