List questions from hermitian-matrices

Published on 23 Feb 2026 - 10:20

98

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Eigenvalues of a block Hermitian matrix

Published on 29 Oct 2022 - 18:54

50

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Show that $|x^\ast Ay|=|x^\ast By|$ iff. $A=e^{i\theta}B$.

Published on 19 Nov 2022 - 13:47

64

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If A,B are hermitian matrices and all eigenvalues of B are positive, then why all eigenvalues of AB are real?

Published on 19 Nov 2022 - 15:26

40

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Let $\hat{A}=\left[\begin{array}{cc}A&y\\y^\ast&a\end{array}\right]$. what's the possible value of rank $\hat{A}$-rank $A$?

Published on 21 Nov 2022 - 2:21

86

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If the matrix exponential is unitary, is the exponent necessarily skew-Hermitian?

Published on 27 Mar 2026 - 4:58

94

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If $A^*= A$ and $A^m= 0$, then $A= 0$.

Published on 26 Mar 2026 - 12:34

30

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Show that $\lambda_{2}(zz^\ast)=\lambda_{n-1}(zz^\ast)=0$.

Published on 08 Dec 2022 - 6:49

65

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For projection matrices, which vector of the outer product should be complex conjugated?

Published on 09 Dec 2022 - 3:58

118

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Are all positive operators Hermitian?

Published on 14 Dec 2022 - 20:42

73

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Why do eigenvalues of Hermitian/Unitary maps have to be distinct for the eigenvectors to be orthogonal?

Published on 21 Dec 2022 - 4:12

44

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numerical radius

Published on 28 Dec 2022 - 20:24

356

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Decomposition of hermitian matrix as difference of positive semidefinite matrices

Published on 27 Mar 2026 - 7:14

76

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Do I have to study Complex Analysis before Hermitian Matrix?

Published on 06 Jan 2023 - 17:29

73

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Canonical form of a hermitian matrix with respect to congruence

Published on 23 Feb 2026 - 4:57

List Question

Derivative of Hermitian sesquilinear form with respect to its own matrix

Eigenvalues of a block Hermitian matrix

Show that $|x^\ast Ay|=|x^\ast By|$ iff. $A=e^{i\theta}B$.

If A,B are hermitian matrices and all eigenvalues of B are positive, then why all eigenvalues of AB are real?

Let $\hat{A}=\left[\begin{array}{cc}A&y\\y^\ast&a\end{array}\right]$. what's the possible value of rank $\hat{A}$-rank $A$?

If the matrix exponential is unitary, is the exponent necessarily skew-Hermitian?

If $A^*= A$ and $A^m= 0$, then $A= 0$.

Show that $\lambda_{2}(zz^\ast)=\lambda_{n-1}(zz^\ast)=0$.

For projection matrices, which vector of the outer product should be complex conjugated?

Are all positive operators Hermitian?

Why do eigenvalues of Hermitian/Unitary maps have to be distinct for the eigenvectors to be orthogonal?

numerical radius

Decomposition of hermitian matrix as difference of positive semidefinite matrices

Do I have to study Complex Analysis before Hermitian Matrix?

Canonical form of a hermitian matrix with respect to congruence

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