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 376 · Answer 1 · 2026-04-15 00:06:54

376

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 15 Apr 2026 - 0:06

score 254 · Answer 2 · 2026-05-07 15:21:07

254

Views

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

Published on 07 May 2026 - 15:21

score 104 · Answer 3 · 2026-05-06 03:52:05

104

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 06 May 2026 - 3:52

score 926 · Answer 4 · 2026-05-07 17:24:32

926

Views

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

Published on 07 May 2026 - 17:24

score 319 · Answer 5 · 2026-05-10 11:02:26

319

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 10 May 2026 - 11:02

score 32 · Answer 6 · 2026-04-17 04:02:34

32

Views

Generating symmetric pascal matrix

Published on 17 Apr 2026 - 4:02

score 74 · Answer 7 · 2026-04-14 15:20:14

74

Views

Integral maximization inequality

Published on 14 Apr 2026 - 15:20

score 477 · Answer 8 · 2026-04-14 02:14:33

477

Views

Symmetric matrix- matrix transpose times matrix decomposition

Published on 14 Apr 2026 - 2:14

score 3k · Answer 9 · 2026-04-15 13:24:29

3k

Views

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

Published on 15 Apr 2026 - 13:24

score 436 · Answer 10 · 2026-04-08 21:55:43

436

Views

Matrix norms using trace

Published on 08 Apr 2026 - 21:55

score 3.5k · Answer 11 · 2026-05-07 07:42:53

3.5k

Views

Symmetric linear transformation has symmetric matrix

Published on 07 May 2026 - 7:42

score 1.1k · Answer 12 · 2026-05-07 10:17:51

1.1k

Views

Find an orthogonal set of eigenvectors

Published on 07 May 2026 - 10:17

score 110 · Answer 13 · 2026-04-12 13:37:54

110

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 12 Apr 2026 - 13:37

score 953 · Answer 14 · 2026-05-10 12:32:49

953

Views

Prove Gaussian elimination preserves positive definiteness

Published on 10 May 2026 - 12:32

score 1.1k · Answer 15 · 2026-04-29 12:52:54

1.1k

Views

Generating a random tridiagonal symmetric positive definite matrix

Published on 29 Apr 2026 - 12:52

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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