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 818 · Answer 1 · 2026-03-25 09:43:10

818

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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 25 Mar 2026 - 9:43

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 942 · Answer 3 · 2018-07-04 12:24:04

942

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

Published on 04 Jul 2018 - 12:24

score 114 · Answer 4 · 2026-03-25 22:09:32

114

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Find symmetric matrix containing no 0's, given eigenvalues

Published on 25 Mar 2026 - 22:09

score 101 · Answer 5 · 2018-07-07 23:06:07

101

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

Published on 07 Jul 2018 - 23:06

score 422 · Answer 6 · 2018-07-08 18:10:52

422

Views

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

Published on 08 Jul 2018 - 18:10

score 707 · Answer 7 · 2026-03-25 21:47:32

707

Views

Proof of a matrix trace inequality

Published on 25 Mar 2026 - 21:47

score 480 · Answer 8 · 2018-07-10 08:31:30

480

Views

Largest eigenvalues of matrix and its doubled symmetric part

Published on 10 Jul 2018 - 8:31

score 1.9k · Answer 9 · 2018-07-12 10:30:58

1.9k

Views

Sampling multivariate normal with low-rank covariance

Published on 12 Jul 2018 - 10:30

score 929 · Answer 10 · 2026-03-25 01:18:48

929

Views

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

Published on 25 Mar 2026 - 1:18

score 89 · Answer 11 · 2018-07-17 10:12:32

89

Views

positive-definite matrix with equal row sums

Published on 17 Jul 2018 - 10:12

score 81 · Answer 12 · 2026-03-25 22:06:06

81

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 25 Mar 2026 - 22:06

score 69 · Answer 13 · 2018-07-22 06:39:46

69

Views

Linear Algebra Proofs (Diction Understanding) for high school student

Published on 22 Jul 2018 - 6:39

score 188 · Answer 14 · 2026-03-25 19:36:53

188

Views

Skew-Symmetric vs Symmetric

Published on 25 Mar 2026 - 19:36

score 99 · Answer 15 · 2026-03-25 17:44:39

99

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 25 Mar 2026 - 17:44

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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