Question

Maximal eigenvalue of Hermitian matrix lies on the diagonal of $A$

score 82 · Answer 1 · 2026-03-25 19:11:45

82

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Maximal eigenvalue of Hermitian matrix lies on the diagonal of $A$

Published on 25 Mar 2026 - 19:11

score 189 · Answer 2 · 2026-03-25 22:10:38

189

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Reflection matrix such that $Ax = y$ and $Ay = x$

Published on 25 Mar 2026 - 22:10

score 61 · Answer 3 · 2026-03-25 22:10:06

61

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Parametrizing Unitary matrices using Hermitian matrices. Covers the whole space?

Published on 25 Mar 2026 - 22:10

score 55 · Answer 4 · 2023-06-14 10:34:22

55

Views

Kähler form on a Hermitian manifold

Published on 14 Jun 2023 - 10:34

score 135 · Answer 5 · 2023-06-18 20:47:03

135

Views

Prove that matrix is Hermitian iff it's equal to its adjoint with general hermitian inner products

Published on 18 Jun 2023 - 20:47

score 42 · Answer 6 · 2023-06-22 15:42:35

42

Views

Showing a recursively defined sequence is positive definite

Published on 22 Jun 2023 - 15:42

score 134 · Answer 7 · 2023-06-27 02:41:06

134

Views

Prove or disprove $\det(6(A^3 + B^3 + C^3)+(A+B+C)^3) \ge 5^2\det(A^2 + B^2 + C^2)\cdot\det(A + B+ C)$

Published on 27 Jun 2023 - 2:41

score 46 · Answer 8 · 2023-07-05 17:56:01

46

Views

signature of hermitian matrix in terms of submatrix determinants

Published on 05 Jul 2023 - 17:56

score 151 · Answer 9 · 2026-03-26 01:11:57

151

Views

If $A$ is Hermitian and $U=(A-iI)(A+iI)^{−1}$ is unitary, then $U-I$ is invertible

Published on 26 Mar 2026 - 1:11

score 50 · Answer 10 · 2023-08-03 23:44:06

50

Views

ordering of eigenvalues for simultaneously diagonalizable matrices

Published on 03 Aug 2023 - 23:44

score 202 · Answer 11 · 2023-08-08 17:52:37

202

Views

Let $A$ be a Hermitian matrix, prove that $v^*Av >0$ for all $0 \not = v \in \Bbb C^n$ $\iff$ all the eigenvalues of $A$ are greater than zero

Published on 08 Aug 2023 - 17:52

score 159 · Answer 12 · 2023-08-11 13:58:56

159

Views

Eigenvalue problem and its complex conjugate

Published on 11 Aug 2023 - 13:58

score 76 · Answer 13 · 2026-02-23 12:08:05

76

Views

Prove: For full rank matrix $A\in\mathbb{C}^{m\times n}$ with $m>n$ and diagonal matrix $B\in\mathbb{C}^{n\times n}$ we have $rank(ABA^H)=n$

Published on 23 Feb 2026 - 12:08

score 94 · Answer 14 · 2023-08-11 19:43:10

94

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Prove: If matrix $A\in\mathbb{C}^{m\times n}$ with $m>n$ is full rank and $B\in\mathbb{C}^{n\times n}$ is diagonal, $ABA^H$ is positive semi-definite

Published on 11 Aug 2023 - 19:43

score 38 · Answer 15 · 2023-09-06 16:52:24

38

Views

Proof that an operator is self-adjoint if and only if its matrix is self-adjoint

Published on 06 Sep 2023 - 16:52

List Question

Maximal eigenvalue of Hermitian matrix lies on the diagonal of $A$

Reflection matrix such that $Ax = y$ and $Ay = x$

Parametrizing Unitary matrices using Hermitian matrices. Covers the whole space?

Kähler form on a Hermitian manifold

Prove that matrix is Hermitian iff it's equal to its adjoint with general hermitian inner products

Showing a recursively defined sequence is positive definite

Prove or disprove $\det(6(A^3 + B^3 + C^3)+(A+B+C)^3) \ge 5^2\det(A^2 + B^2 + C^2)\cdot\det(A + B+ C)$

signature of hermitian matrix in terms of submatrix determinants

If $A$ is Hermitian and $U=(A-iI)(A+iI)^{−1}$ is unitary, then $U-I$ is invertible

ordering of eigenvalues for simultaneously diagonalizable matrices

Let $A$ be a Hermitian matrix, prove that $v^*Av >0$ for all $0 \not = v \in \Bbb C^n$ $\iff$ all the eigenvalues of $A$ are greater than zero

Eigenvalue problem and its complex conjugate

Prove: For full rank matrix $A\in\mathbb{C}^{m\times n}$ with $m>n$ and diagonal matrix $B\in\mathbb{C}^{n\times n}$ we have $rank(ABA^H)=n$

Prove: If matrix $A\in\mathbb{C}^{m\times n}$ with $m>n$ is full rank and $B\in\mathbb{C}^{n\times n}$ is diagonal, $ABA^H$ is positive semi-definite

Proof that an operator is self-adjoint if and only if its matrix is self-adjoint

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