Question

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

score 93 · Answer 1 · 2026-03-25 19:05:38

93

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

Published on 25 Mar 2026 - 19:05

score 67 · Answer 2 · 2026-03-25 19:05:06

67

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

Published on 25 Mar 2026 - 19:05

score 163 · Answer 3 · 2026-03-25 17:36:16

163

Views

The relation between the spectral theorem and unitary diagonalization

Published on 25 Mar 2026 - 17:36

score 43 · Answer 4 · 2026-03-25 19:05:42

43

Views

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

Published on 25 Mar 2026 - 19:05

score 425 · Answer 5 · 2026-03-25 19:04:17

425

Views

The geometry meaning of Unitary matrix/operator

Published on 25 Mar 2026 - 19:04

score 167 · Answer 6 · 2026-03-25 19:00:32

167

Views

A compact normal operator is diagonalisable.

Published on 25 Mar 2026 - 19:00

score 754 · Answer 7 · 2026-04-11 16:58:37

754

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 11 Apr 2026 - 16:58

score 142 · Answer 8 · 2026-03-25 19:07:21

142

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 25 Mar 2026 - 19:07

score 596 · Answer 9 · 2026-03-25 19:04:11

596

Views

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

Published on 25 Mar 2026 - 19:04

score 72 · Answer 10 · 2026-03-25 19:05:43

72

Views

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

Published on 25 Mar 2026 - 19:05

score 28 · Answer 11 · 2026-03-25 20:39:48

28

Views

An exercise about normal operators

Published on 25 Mar 2026 - 20:39

score 47 · Answer 12 · 2026-03-25 18:45:02

47

Views

is this (unbounded) operator normal?

Published on 25 Mar 2026 - 18:45

score 62 · Answer 13 · 2026-03-25 19:02:28

62

Views

Spectral decomposition of a normal operator: non-distinct eigenvalues

Published on 25 Mar 2026 - 19:02

score 53 · Answer 14 · 2026-03-25 19:05:06

53

Views

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

Published on 25 Mar 2026 - 19:05

score 49 · Answer 15 · 2026-03-25 19:04:03

49

Views

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

Published on 25 Mar 2026 - 19:04

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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