Question

How do you prove the adjoint of a linear operator in any abstract inner product space is related to the conjugate transpose of its matrix?

score 532 · Answer 1 · 2026-03-28 00:06:14

532

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How do you prove the adjoint of a linear operator in any abstract inner product space is related to the conjugate transpose of its matrix?

Published on 28 Mar 2026 - 0:06

score 190 · Answer 2 · 2026-03-26 01:28:43

190

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Question 2.18 from Brezis: Would someone help me to understand a solution given to this question?

Published on 26 Mar 2026 - 1:28

score 628 · Answer 3 · 2026-03-27 03:57:46

628

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Unitary operators, inner products and unit operators with Dirac notation

Published on 27 Mar 2026 - 3:57

score 176 · Answer 4 · 2026-03-27 05:41:57

176

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An $n \times n$ matrix with real coefficients is a Gramian matrix if and only if $A$ is symmetric and all its eigenvalues are nonnegative

Published on 27 Mar 2026 - 5:41

score 247 · Answer 5 · 2021-09-17 18:49:03

247

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Nilpotent and adjoint

Published on 17 Sep 2021 - 18:49

score 45 · Answer 6 · 2021-09-18 12:25:09

45

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Powerset Operators Preserve Order

Published on 18 Sep 2021 - 12:25

score 258 · Answer 7 · 2026-03-29 03:03:36

258

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Question 2.22 from Brezis' book of Functional Analysis

Published on 29 Mar 2026 - 3:03

score 121 · Answer 8 · 2026-03-29 03:02:43

121

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Question 2.24 from Brezis' book of Functional Analysis

Published on 29 Mar 2026 - 3:02

score 523 · Answer 9 · 2021-10-02 04:54:33

523

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For the inner product space $V$ and linear transform $g: V \to F$, find vector $y$ such that $g(x) = \langle x, y \rangle$ for $x \in V$-soln adjust

Published on 02 Oct 2021 - 4:54

score 155 · Answer 10 · 2021-10-02 09:42:35

155

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Why is this the adjoint operator?

Published on 02 Oct 2021 - 9:42

score 58 · Answer 11 · 2026-03-28 05:45:51

58

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Is this operator surjective?

Published on 28 Mar 2026 - 5:45

score 38 · Answer 12 · 2021-10-10 04:36:16

38

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Adjoint Operators Between Posets are Unique

Published on 10 Oct 2021 - 4:36

score 38 · Answer 13 · 2021-10-11 18:54:15

38

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Finding the adjoint of $L$ where $Lf = \int_0^T \exp(A(T-t))\pmb b f(t)\;dt$

Published on 11 Oct 2021 - 18:54

score 42 · Answer 14 · 2021-10-16 14:07:34

42

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How to prove that $(\tau^v)^* = \tau^{-v}$ for distributions?

Published on 16 Oct 2021 - 14:07

score 305 · Answer 15 · 2026-03-27 00:56:35

305

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Hermitian vector spaces, dual and adjoint maps

Published on 27 Mar 2026 - 0:56

List Question

How do you prove the adjoint of a linear operator in any abstract inner product space is related to the conjugate transpose of its matrix?

Question 2.18 from Brezis: Would someone help me to understand a solution given to this question?

Unitary operators, inner products and unit operators with Dirac notation

An $n \times n$ matrix with real coefficients is a Gramian matrix if and only if $A$ is symmetric and all its eigenvalues are nonnegative

Nilpotent and adjoint

Powerset Operators Preserve Order

Question 2.22 from Brezis' book of Functional Analysis

Question 2.24 from Brezis' book of Functional Analysis

For the inner product space $V$ and linear transform $g: V \to F$, find vector $y$ such that $g(x) = \langle x, y \rangle$ for $x \in V$-soln adjust

Why is this the adjoint operator?

Is this operator surjective?

Adjoint Operators Between Posets are Unique

Finding the adjoint of $L$ where $Lf = \int_0^T \exp(A(T-t))\pmb b f(t)\;dt$

How to prove that $(\tau^v)^* = \tau^{-v}$ for distributions?

Hermitian vector spaces, dual and adjoint maps

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