Question

Given K s.t. $\frac{K+K^}{2}=L^L+I$ and $\frac{K-K^}{2i}=\frac{L+L^}{2}$, find $L$.

score 26 · Answer 1 · 2021-10-29 10:11:41

26

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Given K s.t. $\frac{K+K^}{2}=L^L+I$ and $\frac{K-K^}{2i}=\frac{L+L^}{2}$, find $L$.

Published on 29 Oct 2021 - 10:11

score 51 · Answer 2 · 2021-11-02 16:22:36

51

Views

How can this be diagonalizable?

Published on 02 Nov 2021 - 16:22

score 238 · Answer 3 · 2021-11-04 18:36:07

238

Views

How to show $BB^\dagger$ is hermitian?

Published on 04 Nov 2021 - 18:36

score 153 · Answer 4 · 2026-03-26 07:35:30

153

Views

Matrix logarithm of unitary matrix from polar decomposition of product of positive definite matrices

Published on 26 Mar 2026 - 7:35

score 84 · Answer 5 · 2021-11-17 10:41:58

84

Views

How to find the restriction of a semidefinite matrix to positive eigenvalues?

Published on 17 Nov 2021 - 10:41

score 48 · Answer 6 · 2021-11-18 17:09:17

48

Views

Hermitian transformation and its minimal polynomial

Published on 18 Nov 2021 - 17:09

score 292 · Answer 7 · 2021-11-21 22:51:31

292

Views

How to show that rank$(A) \geq \frac{|\text{tr}(A)|^2}{\text{tr}(A^*A)}$?

Published on 21 Nov 2021 - 22:51

score 531 · Answer 8 · 2021-11-22 03:35:52

531

Views

Special lower bound on minimum singular value

Published on 22 Nov 2021 - 3:35

score 169 · Answer 9 · 2021-11-22 07:47:08

If $A,B$ are Hermitian, how to show that $\lambda_\max(AB^{-1}) =\max_{x\ne 0} \frac{x^*Ax}{x^*Bx}$ if A,B have only positive eigenvalues?

score 144 · Answer 10 · 2021-11-22 08:32:02

144

Views

how to show that $A=[a_i+a_j]_{ij}$ has exactly one positive and one negative eigenvalue.

Published on 22 Nov 2021 - 8:32

score 44 · Answer 11 · 2021-11-22 09:12:05

44

Views

How to show that $(Re\lambda_1,\dotsb,Re\lambda_n)^T$ is majorized by $(\lambda_1(H),\dotsb,\lambda_n(H))^T$?

Published on 22 Nov 2021 - 9:12

score 31 · Answer 12 · 2021-11-22 17:33:34

31

Views

Change of basis matrix exactly one row away from being correct

Published on 22 Nov 2021 - 17:33

score 43 · Answer 13 · 2021-11-25 15:05:55

43

Views

If two hermitian matricies commute, do they share an orthonormal eigenbasis?

Published on 25 Nov 2021 - 15:05

score 106 · Answer 14 · 2026-03-26 04:32:02

106

Views

Minimal spanning set ("conical basis") for 2x2 Hermitian PSD (positive semi-definite) cone?

Published on 26 Mar 2026 - 4:32

score 223 · Answer 15 · 2021-11-28 21:44:27

223

Views

Can we construct an ORTHOGONAL ($\text{trace}(A^\dagger B) = 0$) basis for Hermitian matrices made of PSD (positive semi-definite) Hermitian matrices?

Published on 28 Nov 2021 - 21:44

List Question

Given K s.t. $\frac{K+K^}{2}=L^L+I$ and $\frac{K-K^}{2i}=\frac{L+L^}{2}$, find $L$.

How can this be diagonalizable?

How to show $BB^\dagger$ is hermitian?

Matrix logarithm of unitary matrix from polar decomposition of product of positive definite matrices

How to find the restriction of a semidefinite matrix to positive eigenvalues?

Hermitian transformation and its minimal polynomial

How to show that rank$(A) \geq \frac{|\text{tr}(A)|^2}{\text{tr}(A^*A)}$?

Special lower bound on minimum singular value

If $A,B$ are Hermitian, how to show that $\lambda_\max(AB^{-1}) =\max_{x\ne 0} \frac{x^Ax}{x^Bx}$ if A,B have only positive eigenvalues?

how to show that $A=[a_i+a_j]_{ij}$ has exactly one positive and one negative eigenvalue.

How to show that $(Re\lambda_1,\dotsb,Re\lambda_n)^T$ is majorized by $(\lambda_1(H),\dotsb,\lambda_n(H))^T$?

Change of basis matrix exactly one row away from being correct

If two hermitian matricies commute, do they share an orthonormal eigenbasis?

Minimal spanning set ("conical basis") for 2x2 Hermitian PSD (positive semi-definite) cone?

Can we construct an ORTHOGONAL ($\text{trace}(A^\dagger B) = 0$) basis for Hermitian matrices made of PSD (positive semi-definite) Hermitian matrices?

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