Question

What is an example of a symmetric operator with non-real spectrum?

score 339 · Answer 1 · 2026-03-25 16:13:40

339

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What is an example of a symmetric operator with non-real spectrum?

Published on 25 Mar 2026 - 16:13

score 2.5k · Answer 2 · 2016-12-09 00:36:56

2.5k

Views

Spectrum for a bounded linear operator and its adjoint on a Banach space are same.

Published on 09 Dec 2016 - 0:36

score 64 · Answer 3 · 2016-12-11 00:22:07

64

Views

A diagonalizable operator with positive eigenvalues and existence of a projection as a limit

Published on 11 Dec 2016 - 0:22

score 89 · Answer 4 · 2016-12-17 00:45:49

89

Views

Complete blocks of projections and spectral theorem

Published on 17 Dec 2016 - 0:45

score 475 · Answer 5 · 2016-12-18 17:51:23

475

Views

Resolvent set and spectrum of operator $T : C[-1,3] \rightarrow C[-1,3]$, where $Tx(t) = tx(t)$

Published on 18 Dec 2016 - 17:51

score 115 · Answer 6 · 2016-12-19 12:15:53

115

Views

How to prove the the spectral radius is positive and the associated eigenvector has positive components?

Published on 19 Dec 2016 - 12:15

score 685 · Answer 7 · 2026-03-29 13:40:58

685

Views

Why is the spectrum of the Laplace operator positive?

Published on 29 Mar 2026 - 13:40

score 55 · Answer 8 · 2016-12-21 07:07:16

55

Views

If $(Tx)(t)=\alpha(t)x(t)$ is compact on $L^2[a,b]$, then $\alpha(t)=0$ a.e. on $[a,b]$

Published on 21 Dec 2016 - 7:07

score 80 · Answer 9 · 2026-03-25 13:51:59

80

Views

Showing that we can write $E_{\lambda}=I-E^{+}_{\lambda}$.

Published on 25 Mar 2026 - 13:51

score 517 · Answer 10 · 2026-03-28 16:14:13

517

Views

Do the eigenvalues of the product of a positive diagonal matrix and a skew-symmetric matrix still have zero real part?

Published on 28 Mar 2026 - 16:14

score 258 · Answer 11 · 2016-12-29 20:46:57

258

Views

Do two matrices close in spectral norm have close traces?

Published on 29 Dec 2016 - 20:46

score 30 · Answer 12 · 2016-12-30 06:43:15

30

Views

How to prove $\rho(A^{-1}N)=\rho(A^{-1})\rho(N)$?

Published on 30 Dec 2016 - 6:43

score 2.1k · Answer 13 · 2016-12-30 20:38:23

2.1k

Views

Weaker Assumption for Convergence of the Neumann series

Published on 30 Dec 2016 - 20:38

score 442 · Answer 14 · 2017-01-05 16:47:16

442

Views

Infer signs of generalized eigenvalues of $(A,B)$ for real $PSD$ $ A$ and real symmetric $B$

Published on 05 Jan 2017 - 16:47

score 1.6k · Answer 15 · 2026-03-26 02:52:58

1.6k

Views

Complex hermite polynomials as an eigenfunction of an operator?

Published on 26 Mar 2026 - 2:52

List Question

What is an example of a symmetric operator with non-real spectrum?

Spectrum for a bounded linear operator and its adjoint on a Banach space are same.

A diagonalizable operator with positive eigenvalues and existence of a projection as a limit

Complete blocks of projections and spectral theorem

Resolvent set and spectrum of operator $T : C[-1,3] \rightarrow C[-1,3]$, where $Tx(t) = tx(t)$

How to prove the the spectral radius is positive and the associated eigenvector has positive components?

Why is the spectrum of the Laplace operator positive?

If $(Tx)(t)=\alpha(t)x(t)$ is compact on $L^2[a,b]$, then $\alpha(t)=0$ a.e. on $[a,b]$

Showing that we can write $E_{\lambda}=I-E^{+}_{\lambda}$.

Do the eigenvalues of the product of a positive diagonal matrix and a skew-symmetric matrix still have zero real part?

Do two matrices close in spectral norm have close traces?

How to prove $\rho(A^{-1}N)=\rho(A^{-1})\rho(N)$?

Weaker Assumption for Convergence of the Neumann series

Infer signs of generalized eigenvalues of $(A,B)$ for real $PSD$ $ A$ and real symmetric $B$

Complex hermite polynomials as an eigenfunction of an operator?

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