Question

$T$ is a normal operator, prove any eigenspace of $T+T^*$ is invariant under $T$

score 92 · Answer 1 · 2020-06-29 16:46:26

92

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$T$ is a normal operator, prove any eigenspace of $T+T^*$ is invariant under $T$

Published on 29 Jun 2020 - 16:46

score 66 · Answer 2 · 2020-07-09 19:39:10

66

Views

If $0 \in \sigma(N)$ and $A = NN^\ast$, then $0 \in \sigma(A)$.

Published on 09 Jul 2020 - 19:39

score 162 · Answer 3 · 2020-07-18 13:19:29

162

Views

The relation between the spectral theorem and unitary diagonalization

Published on 18 Jul 2020 - 13:19

score 42 · Answer 4 · 2020-07-18 21:31:15

42

Views

how many normal operators $T$ that satisfy the following conditions are existing?

Published on 18 Jul 2020 - 21:31

score 424 · Answer 5 · 2020-07-20 20:52:16

424

Views

The geometry meaning of Unitary matrix/operator

Published on 20 Jul 2020 - 20:52

score 166 · Answer 6 · 2020-07-21 18:09:45

166

Views

A compact normal operator is diagonalisable.

Published on 21 Jul 2020 - 18:09

score 751 · Answer 7 · 2016-08-29 13:30:20

751

Views

$V$ be a finite dimensional complex inner product space , $T$ be a normal operator on $V$ such that $T^*T=T^2$ , then is $T$ self-adjoint?

Published on 29 Aug 2016 - 13:30

score 141 · Answer 8 · 2016-09-02 11:40:29

141

Views

$V$ be a complex i.p.s. of dimension $n$ , $f(x) \in \mathcal P_{n-1}(\mathbb C)$ then $\exists $ linear operator $T$ on $V$ s.t. $T^*=f(T)$?

Published on 02 Sep 2016 - 11:40

score 595 · Answer 9 · 2016-11-04 01:28:20

595

Views

characteristic vectors for $Τ$ which are associated with distinct characteristic values are orthogonal

Published on 04 Nov 2016 - 1:28

score 71 · Answer 10 · 2023-04-03 00:30:34

71

Views

Ambiguous step in theorem 7.20 of Sheldon Axler’s Linear Algebra Done Right 3rd ed.

Published on 03 Apr 2023 - 0:30

score 27 · Answer 11 · 2023-05-31 07:41:47

27

Views

An exercise about normal operators

Published on 31 May 2023 - 7:41

score 46 · Answer 12 · 2023-06-03 10:24:45

46

Views

is this (unbounded) operator normal?

Published on 03 Jun 2023 - 10:24

score 61 · Answer 13 · 2023-06-05 12:39:03

61

Views

Spectral decomposition of a normal operator: non-distinct eigenvalues

Published on 05 Jun 2023 - 12:39

score 52 · Answer 14 · 2023-06-18 04:00:17

52

Views

Equivalent criterion for invertiblity of a normal operator in an Hilbert space.

Published on 18 Jun 2023 - 4:00

score 48 · Answer 15 · 2023-06-28 13:17:14

48

Views

Prove the operator $f$ is normal with the expression of the operator

Published on 28 Jun 2023 - 13:17

List Question

$T$ is a normal operator, prove any eigenspace of $T+T^*$ is invariant under $T$

If $0 \in \sigma(N)$ and $A = NN^\ast$, then $0 \in \sigma(A)$.

The relation between the spectral theorem and unitary diagonalization

how many normal operators $T$ that satisfy the following conditions are existing?

The geometry meaning of Unitary matrix/operator

A compact normal operator is diagonalisable.

$V$ be a finite dimensional complex inner product space , $T$ be a normal operator on $V$ such that $T^*T=T^2$ , then is $T$ self-adjoint?

$V$ be a complex i.p.s. of dimension $n$ , $f(x) \in \mathcal P_{n-1}(\mathbb C)$ then $\exists $ linear operator $T$ on $V$ s.t. $T^*=f(T)$?

characteristic vectors for $Τ$ which are associated with distinct characteristic values are orthogonal

Ambiguous step in theorem 7.20 of Sheldon Axler’s Linear Algebra Done Right 3rd ed.

An exercise about normal operators

is this (unbounded) operator normal?

Spectral decomposition of a normal operator: non-distinct eigenvalues

Equivalent criterion for invertiblity of a normal operator in an Hilbert space.

Prove the operator $f$ is normal with the expression of the operator

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