List questions from spectral-theory

Published on 25 Mar 2026 - 17:17

66

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Does $\sup_{\Vert x \rVert = 1} \langle A x, x \rangle$ equal the largest eigenvalue of $A$?

Published on 25 Mar 2026 - 11:11

153

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Why the Markov chain transition matrix doesn't have an eigenvalue $\lambda=1$?

Published on 26 Mar 2026 - 6:33

43

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Let $U$ be a normal operator. Prove, that there exists a sequence $\{ U_n \}$ which converges to $U$ uniformly.

Published on 10 Feb 2023 - 12:27

68

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What is the "spectral representation of unitary operators"?

Published on 10 Feb 2023 - 16:40

44

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Quantum Mechanical PDE Question

Published on 30 Mar 2026 - 2:57

57

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How to use Spectral theorem in this proof?

Published on 28 Mar 2026 - 4:33

92

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Show that $\sigma(a+\lambda b) = \sigma(a) + \lambda \sigma(b)$, for all $\lambda \in \mathbb{C}$.

Published on 28 Mar 2026 - 3:25

222

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Show that $U$ commutes with $T$ if and only if $U$ commutes with each $T_i$

Published on 17 Feb 2023 - 6:10

103

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spectral bound for symmetric matrices

Published on 19 Feb 2023 - 19:59

71

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Sequence of Dirichlet eigenvalues of monotone cover converges to Dirichlet eigenvalues of limit

Published on 29 Mar 2026 - 23:30

53

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Bounded operator with finite continuous spectrum

Published on 05 Mar 2023 - 4:26

71

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Spectrum of $A u=i u^{\prime}$ on differing domains in $L^2([0,1])$

Published on 05 Mar 2023 - 20:05

170

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Spectrum of the discrete laplacian $\delta$ on $l^2(\mathbb{Z})$

Published on 29 Mar 2026 - 23:30

408

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The spectrum of the right shift operator on $\ell^2(\mathbb{Z}$)

Published on 07 Mar 2023 - 1:08

List Question

Densely defined and closed operator

Does $\sup_{\Vert x \rVert = 1} \langle A x, x \rangle$ equal the largest eigenvalue of $A$?

Why the Markov chain transition matrix doesn't have an eigenvalue $\lambda=1$?

Let $U$ be a normal operator. Prove, that there exists a sequence $\{ U_n \}$ which converges to $U$ uniformly.

What is the "spectral representation of unitary operators"?

Quantum Mechanical PDE Question

How to use Spectral theorem in this proof?

Show that $\sigma(a+\lambda b) = \sigma(a) + \lambda \sigma(b)$, for all $\lambda \in \mathbb{C}$.

Show that $U$ commutes with $T$ if and only if $U$ commutes with each $T_i$

spectral bound for symmetric matrices

Sequence of Dirichlet eigenvalues of monotone cover converges to Dirichlet eigenvalues of limit

Bounded operator with finite continuous spectrum

Spectrum of $A u=i u^{\prime}$ on differing domains in $L^2([0,1])$

Spectrum of the discrete laplacian $\delta$ on $l^2(\mathbb{Z})$

The spectrum of the right shift operator on $\ell^2(\mathbb{Z}$)

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