Question

Let $T$ be a self-adjoint operator on $V$ where $\beta$ is a basis for $V$. The matrix of $T$ is Hermitian if and only if $\beta$ is orthonormal.

score 373 · Answer 1 · 2018-04-06 22:04:23

373

Views

Let $T$ be a self-adjoint operator on $V$ where $\beta$ is a basis for $V$. The matrix of $T$ is Hermitian if and only if $\beta$ is orthonormal.

Published on 06 Apr 2018 - 22:04

score 249 · Answer 2 · 2018-04-10 12:18:26

249

Views

How to differentiate an expression with respect to a symmetric matrix?

Published on 10 Apr 2018 - 12:18

score 96 · Answer 3 · 2026-03-17 11:12:11

96

Views

Can any linear map, $\phi$, can be expressed a as $\phi = S + N - N^T,$ where $S$ is a self-adjoint and $N$ is a nilpotent map

Published on 17 Mar 2026 - 11:12

score 921 · Answer 4 · 2018-04-13 10:43:18

921

Views

Rank of the sum of an all-ones matrix and an identity matrix

Published on 13 Apr 2018 - 10:43

score 318 · Answer 5 · 2026-03-24 20:32:10

318

Views

Find necessary and sufficient conditions on $a,b,c$ such that the matrix $\begin{bmatrix}a & b\\b & c\end{bmatrix}$ has a factorization $LL^{T}$

Published on 24 Mar 2026 - 20:32

score 26 · Answer 6 · 2026-03-22 04:47:53

26

Views

Generating symmetric pascal matrix

Published on 22 Mar 2026 - 4:47

score 70 · Answer 7 · 2026-03-22 02:59:57

70

Views

Integral maximization inequality

Published on 22 Mar 2026 - 2:59

score 475 · Answer 8 · 2026-03-25 03:07:04

475

Views

Symmetric matrix- matrix transpose times matrix decomposition

Published on 25 Mar 2026 - 3:07

score 3k · Answer 9 · 2026-03-25 06:06:47

3k

Views

Show the rank of A equals to the number of non-zero eigenvalues of $A^TA$

Published on 25 Mar 2026 - 6:06

score 432 · Answer 10 · 2026-03-21 22:27:50

432

Views

Matrix norms using trace

Published on 21 Mar 2026 - 22:27

score 3.5k · Answer 11 · 2018-04-19 08:57:42

3.5k

Views

Symmetric linear transformation has symmetric matrix

Published on 19 Apr 2018 - 8:57

score 1.1k · Answer 12 · 2026-03-22 11:52:04

1.1k

Views

Find an orthogonal set of eigenvectors

Published on 22 Mar 2026 - 11:52

score 108 · Answer 13 · 2026-03-25 12:49:44

108

Views

" Let $A$ be a symmetric $2 \times 2$ matrix with the property $A^{-1} = A$. Find all possible trace values of $\operatorname{tr}A$"

Published on 25 Mar 2026 - 12:49

score 947 · Answer 14 · 2026-03-25 06:01:46

947

Views

Prove Gaussian elimination preserves positive definiteness

Published on 25 Mar 2026 - 6:01

score 1.1k · Answer 15 · 2026-03-22 18:30:14

1.1k

Views

Generating a random tridiagonal symmetric positive definite matrix

Published on 22 Mar 2026 - 18:30

List Question

Let $T$ be a self-adjoint operator on $V$ where $\beta$ is a basis for $V$. The matrix of $T$ is Hermitian if and only if $\beta$ is orthonormal.

How to differentiate an expression with respect to a symmetric matrix?

Can any linear map, $\phi$, can be expressed a as $\phi = S + N - N^T,$ where $S$ is a self-adjoint and $N$ is a nilpotent map

Rank of the sum of an all-ones matrix and an identity matrix

Find necessary and sufficient conditions on $a,b,c$ such that the matrix $\begin{bmatrix}a & b\\b & c\end{bmatrix}$ has a factorization $LL^{T}$

Generating symmetric pascal matrix

Integral maximization inequality

Symmetric matrix- matrix transpose times matrix decomposition

Show the rank of A equals to the number of non-zero eigenvalues of $A^TA$

Matrix norms using trace

Symmetric linear transformation has symmetric matrix

Find an orthogonal set of eigenvectors

" Let $A$ be a symmetric $2 \times 2$ matrix with the property $A^{-1} = A$. Find all possible trace values of $\operatorname{tr}A$"

Prove Gaussian elimination preserves positive definiteness

Generating a random tridiagonal symmetric positive definite matrix

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