Question

How to prove that every dual linear operator of an operator on $L_2(\mathbb{R})$ shares its eigenvalues with its dual operator

score 486 · Answer 1 · 2026-02-26 02:45:26

486

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How to prove that every dual linear operator of an operator on $L_2(\mathbb{R})$ shares its eigenvalues with its dual operator

Published on 26 Feb 2026 - 2:45

score 196 · Answer 2 · 2020-08-11 22:32:09

196

Views

Show that $c=\det f$ with $f: V \to V$ is a linear transformation.

Published on 11 Aug 2020 - 22:32

score 853 · Answer 3 · 2020-10-05 21:31:27

853

Views

Is rank$(T)$=rank$(T^*)$ even if $T:V\to W$ and $W$ not finite dimensional?

Published on 05 Oct 2020 - 21:31

score 132 · Answer 4 · 2020-10-07 23:04:05

132

Views

Definition of composition used in Axler's proof 3.101, Algebraic Properties of Dual Maps

Published on 07 Oct 2020 - 23:04

score 37 · Answer 5 · 2020-10-12 01:38:09

37

Views

proof of surjectivity of dualT implies injectivity of T and conversely

Published on 12 Oct 2020 - 1:38

score 56 · Answer 6 · 2021-01-11 03:43:06

56

Views

Give example(s) of elements that inside torsion part of cohomology group after quotient

Published on 11 Jan 2021 - 3:43

score 278 · Answer 7 · 2021-01-22 20:42:50

278

Views

Is that true that for every linear transformation $\phi : V^* \to W^$ there is a linear transformation $\psi: W \to V$ such that $\psi^ = \phi$?

Published on 22 Jan 2021 - 20:42

score 153 · Answer 8 · 2021-01-25 19:26:32

153

Views

Proving that the curvature of the induced connection satisfies $k_{\nabla^{}}(X,Y) = k_{\nabla}(X, Y)^{}$.

Published on 25 Jan 2021 - 19:26

score 44 · Answer 9 · 2026-03-24 21:09:48

44

Views

Dual linear map

Published on 24 Mar 2026 - 21:09

score 125 · Answer 10 · 2021-03-12 01:04:37

125

Views

Derivation of Dual Curve for Parametric Equations

Published on 12 Mar 2021 - 1:04

score 295 · Answer 11 · 2021-05-11 15:20:12

295

Views

Prove that if $\phi$ is injective then the dual function $\phi^{*}$ is surjective

Published on 11 May 2021 - 15:20

score 518 · Answer 12 · 2021-06-03 16:06:16

518

Views

Matrix representation of adjoint & co-adjoint orbit of $so(3)$

Published on 03 Jun 2021 - 16:06

score 41 · Answer 13 · 2021-09-26 10:09:47

41

Views

Annihilator of $H^p$ is isometrically isomorphic to $H_{0}^{q}$

Published on 26 Sep 2021 - 10:09

score 80 · Answer 14 · 2021-12-15 22:18:03

80

Views

Is there standard mathematical terminology for structures that come in one-to-one pairs?

Published on 15 Dec 2021 - 22:18

score 35 · Answer 15 · 2022-02-05 14:15:04

35

Views

Defining De Morgan dual using $\neg: \mathbf{A}^{\text{op}} \to \mathbf{A}$

Published on 05 Feb 2022 - 14:15

List Question

How to prove that every dual linear operator of an operator on $L_2(\mathbb{R})$ shares its eigenvalues with its dual operator

Show that $c=\det f$ with $f: V \to V$ is a linear transformation.

Is rank$(T)$=rank$(T^*)$ even if $T:V\to W$ and $W$ not finite dimensional?

Definition of composition used in Axler's proof 3.101, Algebraic Properties of Dual Maps

proof of surjectivity of dualT implies injectivity of T and conversely

Give example(s) of elements that inside torsion part of cohomology group after quotient

Is that true that for every linear transformation $\phi : V^* \to W^$ there is a linear transformation $\psi: W \to V$ such that $\psi^ = \phi$?

Proving that the curvature of the induced connection satisfies $k_{\nabla^{}}(X,Y) = k_{\nabla}(X, Y)^{}$.

Dual linear map

Derivation of Dual Curve for Parametric Equations

Prove that if $\phi$ is injective then the dual function $\phi^{*}$ is surjective

Matrix representation of adjoint & co-adjoint orbit of $so(3)$

Annihilator of $H^p$ is isometrically isomorphic to $H_{0}^{q}$

Is there standard mathematical terminology for structures that come in one-to-one pairs?

Defining De Morgan dual using $\neg: \mathbf{A}^{\text{op}} \to \mathbf{A}$

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