Question

Let $A\in\mathbb{R}^{n\times n}$ be positive definite and symmetric. Show that $\langle x,y \rangle_A:=\langle Ax,y \rangle$ defines an inner product.

score 821 · Answer 1 · 2026-05-11 02:50:26

821

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Let $A\in\mathbb{R}^{n\times n}$ be positive definite and symmetric. Show that $\langle x,y \rangle_A:=\langle Ax,y \rangle$ defines an inner product.

Published on 11 May 2026 - 2:50

score 306 · Answer 2 · 2026-03-25 06:03:28

306

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If ${\bf M}_{ij} = \min\{x_i,x_j\}$, is ${\bf M}$ positive semidefinite?

Published on 25 Mar 2026 - 6:03

score 945 · Answer 3 · 2026-04-11 15:43:14

945

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Solving the trace optimization problem $L\Sigma L^T$ for symmetric matrices

Published on 11 Apr 2026 - 15:43

score 117 · Answer 4 · 2026-05-10 17:59:36

117

Views

Find symmetric matrix containing no 0's, given eigenvalues

Published on 10 May 2026 - 17:59

score 104 · Answer 5 · 2026-04-12 07:55:49

104

Views

What is the eigenvalue perturbation if a row-column pair is changed?

Published on 12 Apr 2026 - 7:55

score 425 · Answer 6 · 2026-04-12 21:50:22

425

Views

How do the eigenvalues of $A$ relate to $DAD$ where $A$ is symmetric and $D$ is diagonal?

Published on 12 Apr 2026 - 21:50

score 709 · Answer 7 · 2026-04-11 08:18:50

709

Views

Proof of a matrix trace inequality

Published on 11 Apr 2026 - 8:18

score 483 · Answer 8 · 2026-04-11 04:38:35

483

Views

Largest eigenvalues of matrix and its doubled symmetric part

Published on 11 Apr 2026 - 4:38

score 1.9k · Answer 9 · 2026-04-14 08:21:21

1.9k

Views

Sampling multivariate normal with low-rank covariance

Published on 14 Apr 2026 - 8:21

score 930 · Answer 10 · 2026-05-11 02:50:04

930

Views

Is the positive semidefinite cone still self-dual in the larger vector space of all real $n \times n$ matrices?

Published on 11 May 2026 - 2:50

score 92 · Answer 11 · 2026-04-14 09:12:51

92

Views

positive-definite matrix with equal row sums

Published on 14 Apr 2026 - 9:12

score 84 · Answer 12 · 2026-05-10 18:06:33

84

Views

If $\sigma:M_3\rightarrow S_3$ is a linear map such that $\sigma(PMP^{-1})=P\sigma(M)P^{-1}$, then $\sigma(M)=\ldots$

Published on 10 May 2026 - 18:06

score 72 · Answer 13 · 2026-04-12 01:12:03

72

Views

Linear Algebra Proofs (Diction Understanding) for high school student

Published on 12 Apr 2026 - 1:12

score 191 · Answer 14 · 2026-04-23 16:43:22

191

Views

Skew-Symmetric vs Symmetric

Published on 23 Apr 2026 - 16:43

score 102 · Answer 15 · 2026-05-10 14:49:16

102

Views

If $|A_{ij}|\leq 1$ for all entries of symmetric $A$, then the largest possible spectral norm of $A$ is smaller than $n$?

Published on 10 May 2026 - 14:49

List Question

Let $A\in\mathbb{R}^{n\times n}$ be positive definite and symmetric. Show that $\langle x,y \rangle_A:=\langle Ax,y \rangle$ defines an inner product.

If ${\bf M}_{ij} = \min\{x_i,x_j\}$, is ${\bf M}$ positive semidefinite?

Solving the trace optimization problem $L\Sigma L^T$ for symmetric matrices

Find symmetric matrix containing no 0's, given eigenvalues

What is the eigenvalue perturbation if a row-column pair is changed?

How do the eigenvalues of $A$ relate to $DAD$ where $A$ is symmetric and $D$ is diagonal?

Proof of a matrix trace inequality

Largest eigenvalues of matrix and its doubled symmetric part

Sampling multivariate normal with low-rank covariance

Is the positive semidefinite cone still self-dual in the larger vector space of all real $n \times n$ matrices?

positive-definite matrix with equal row sums

If $\sigma:M_3\rightarrow S_3$ is a linear map such that $\sigma(PMP^{-1})=P\sigma(M)P^{-1}$, then $\sigma(M)=\ldots$

Linear Algebra Proofs (Diction Understanding) for high school student

Skew-Symmetric vs Symmetric

If $|A_{ij}|\leq 1$ for all entries of symmetric $A$, then the largest possible spectral norm of $A$ is smaller than $n$?

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