Question

Does the Schmidt decomposition still hold in infinite dimension?

score 233 · Answer 1 · 2017-08-01 13:31:58

233

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Does the Schmidt decomposition still hold in infinite dimension?

Published on 01 Aug 2017 - 13:31

score 2.4k · Answer 2 · 2017-08-21 08:05:31

2.4k

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singluar values unchanged when multiplied with an orthogonal matrix?

Published on 21 Aug 2017 - 8:05

score 1.3k · Answer 3 · 2017-08-27 17:59:07

1.3k

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When is the algebraic polar decomposition (A=QS) possible?

Published on 27 Aug 2017 - 17:59

score 67 · Answer 4 · 2017-09-08 04:04:58

67

Views

Prove $\|A\|_2 \le |s|$ if and only if $s^2I-A^TA$ is positive semi-definite where $A \in R^{p \times q}$

Published on 08 Sep 2017 - 4:04

score 51 · Answer 5 · 2017-09-18 22:03:26

51

Views

Does "singular" have a common meaning across matrices, decomposition, vectors and values?

Published on 18 Sep 2017 - 22:03

score 221 · Answer 6 · 2026-03-25 17:53:07

221

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Give a vector pair $(b,δb)$ for which $\dfrac{\|δx\|_2}{\|x\|_2}=k_2(A)\dfrac{\|δb\|_2}{\|b\|_2}$ holds

Published on 25 Mar 2026 - 17:53

score 285 · Answer 7 · 2017-09-21 20:25:18

285

Views

How many numbers needed to describe a matrix?

Published on 21 Sep 2017 - 20:25

score 227 · Answer 8 · 2017-09-26 15:26:24

227

Views

Why are these equivalent statements about the largest singular value for matrix $A$? $\sigma \le \,k$ IFF $A^T A \le k^2 I$

Published on 26 Sep 2017 - 15:26

score 1k · Answer 9 · 2017-09-27 00:14:47

1k

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Show adding rows to a non-singular square matrix will keep or increase its minimum singular value

Published on 27 Sep 2017 - 0:14

score 4.4k · Answer 10 · 2017-09-27 20:06:02

4.4k

Views

Singular values of $AB$ and $BA$ where $A$ and $B$ are rectangular matrices

Published on 27 Sep 2017 - 20:06

score 284 · Answer 11 · 2017-09-28 00:25:49

284

Views

Singular Value Theory

Published on 28 Sep 2017 - 0:25

score 116 · Answer 12 · 2017-09-28 17:52:25

116

Views

Extending the Fan-Hoffman singular value inequality for traceless Hermitian matrices

Published on 28 Sep 2017 - 17:52

score 964 · Answer 13 · 2017-10-08 21:36:21

964

Views

If the absolute value of every eigenvalue of a matrix is smaller than 1, is the maximum singular value smaller than 1?

Published on 08 Oct 2017 - 21:36

score 499 · Answer 14 · 2017-10-15 00:42:26

499

Views

Singular values uniquely determined for a matrix, does that mean $A=B$ IFF $\Sigma_A=\Sigma_B$?

Published on 15 Oct 2017 - 0:42

score 163 · Answer 15 · 2017-10-17 14:20:22

163

Views

Maximum determinant of a sum subject to singular value constraint

Published on 17 Oct 2017 - 14:20

List Question

Does the Schmidt decomposition still hold in infinite dimension?

singluar values unchanged when multiplied with an orthogonal matrix?

When is the algebraic polar decomposition (A=QS) possible?

Prove $\|A\|_2 \le |s|$ if and only if $s^2I-A^TA$ is positive semi-definite where $A \in R^{p \times q}$

Does "singular" have a common meaning across matrices, decomposition, vectors and values?

Give a vector pair $(b,δb)$ for which $\dfrac{\|δx\|_2}{\|x\|_2}=k_2(A)\dfrac{\|δb\|_2}{\|b\|_2}$ holds

How many numbers needed to describe a matrix?

Why are these equivalent statements about the largest singular value for matrix $A$? $\sigma \le \,k$ IFF $A^T A \le k^2 I$

Show adding rows to a non-singular square matrix will keep or increase its minimum singular value

Singular values of $AB$ and $BA$ where $A$ and $B$ are rectangular matrices

Singular Value Theory

Extending the Fan-Hoffman singular value inequality for traceless Hermitian matrices

If the absolute value of every eigenvalue of a matrix is smaller than 1, is the maximum singular value smaller than 1?

Singular values uniquely determined for a matrix, does that mean $A=B$ IFF $\Sigma_A=\Sigma_B$?

Maximum determinant of a sum subject to singular value constraint

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