Question

Bounding area of the image of a parallelogram under $M \in GL(n,\mathbb{R})$, $n>2$, using singular values

score 26 · Answer 1 · 2022-05-05 17:50:29

26

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Bounding area of the image of a parallelogram under $M \in GL(n,\mathbb{R})$, $n>2$, using singular values

Published on 05 May 2022 - 17:50

score 237 · Answer 2 · 2022-05-06 11:59:33

237

Views

Limit of the smallest eigenvalue of a random Gram matrix $XX^T/n$.

Published on 06 May 2022 - 11:59

score 73 · Answer 3 · 2022-05-08 14:15:18

73

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Eigenvalues of sum $\lambda_i(X(D_1 + D_2)X^T) = \lambda_{\sigma_1(i)}(XD_1X^T) + \lambda_{\sigma_2(i)}(XD_2X^T)$ where $D_1, D_2$ are diagonal.

Published on 08 May 2022 - 14:15

score 515 · Answer 4 · 2022-05-17 01:00:27

515

Views

Singular values of a product of matrices

Published on 17 May 2022 - 1:00

score 112 · Answer 5 · 2022-05-20 05:24:36

112

Views

Aren't all eigenvalues of $T^*T$ non-negative? (Clarification regarding the definition of singular values)

Published on 20 May 2022 - 5:24

score 51 · Answer 6 · 2022-05-30 17:13:08

51

Views

Proving $K_2(A)=\frac{\sqrt{\max_i|\lambda_i(A^\top A)}|}{\sqrt{\min_i|\lambda_i(A^\top A)|}}$ without using singular values

Published on 30 May 2022 - 17:13

score 121 · Answer 7 · 2026-02-25 07:55:34

121

Views

Generate singular values of a matrix(Gaussian Random) using Quadrant law in python.

Published on 25 Feb 2026 - 7:55

score 78 · Answer 8 · 2022-06-06 07:49:55

78

Views

The eigenvalue/singular values of (large) square random matrices

Published on 06 Jun 2022 - 7:49

score 51 · Answer 9 · 2026-03-25 20:08:37

51

Views

Condition on singular values of two matrices

Published on 25 Mar 2026 - 20:08

score 65 · Answer 10 · 2022-06-28 02:58:30

65

Views

Condition for $(I+\epsilon A)(I+\epsilon A^\top)>\epsilon^2 AA^\top$

Published on 28 Jun 2022 - 2:58

score 59 · Answer 11 · 2022-07-05 17:49:40

59

Views

SVD analysis of the error of the Linear Equation System solutions under random perturbations

Published on 05 Jul 2022 - 17:49

score 88 · Answer 12 · 2026-03-26 08:00:54

88

Views

Proof of "The sum of squared distances from the points to the line is a minimum"

Published on 26 Mar 2026 - 8:00

score 61 · Answer 13 · 2026-03-26 04:53:39

61

Views

Proof that $\Delta A := -\sigma_n u_n {v^T}_n$ is the smallest possible perturbation such that $A + \Delta A$ is singular.

Published on 26 Mar 2026 - 4:53

score 287 · Answer 14 · 2022-08-30 14:34:08

287

Views

Singular value of block matrix and its submatrix

Published on 30 Aug 2022 - 14:34

score 174 · Answer 15 · 2022-09-09 02:25:39

174

Views

Bound on product of matrices

Published on 09 Sep 2022 - 2:25

List Question

Bounding area of the image of a parallelogram under $M \in GL(n,\mathbb{R})$, $n>2$, using singular values

Limit of the smallest eigenvalue of a random Gram matrix $XX^T/n$.

Eigenvalues of sum $\lambda_i(X(D_1 + D_2)X^T) = \lambda_{\sigma_1(i)}(XD_1X^T) + \lambda_{\sigma_2(i)}(XD_2X^T)$ where $D_1, D_2$ are diagonal.

Singular values of a product of matrices

Aren't all eigenvalues of $T^*T$ non-negative? (Clarification regarding the definition of singular values)

Proving $K_2(A)=\frac{\sqrt{\max_i|\lambda_i(A^\top A)}|}{\sqrt{\min_i|\lambda_i(A^\top A)|}}$ without using singular values

Generate singular values of a matrix(Gaussian Random) using Quadrant law in python.

The eigenvalue/singular values of (large) square random matrices

Condition on singular values of two matrices

Condition for $(I+\epsilon A)(I+\epsilon A^\top)>\epsilon^2 AA^\top$

SVD analysis of the error of the Linear Equation System solutions under random perturbations

Proof of "The sum of squared distances from the points to the line is a minimum"

Proof that $\Delta A := -\sigma_n u_n {v^T}_n$ is the smallest possible perturbation such that $A + \Delta A$ is singular.

Singular value of block matrix and its submatrix

Bound on product of matrices

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