List questions from dual-spaces

Published on 11 Jan 2021 - 20:41

62

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Coordinates of a functional in dual space with one qiven coordinate.

Published on 15 Jan 2021 - 19:59

59

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Proof that the canonical mapping of $V$ into $V^{**}$ is not bijective

Published on 16 Jan 2021 - 18:57

213

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Prove that the map $A \mapsto (B \mapsto \operatorname{trace}(AB))$ is an isomorphism $\operatorname{Mat}_{n,m}(K) \to \operatorname{Mat}_{m,n}(K)^*$

Published on 17 Jan 2021 - 20:09

72

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Condition for a finite sequence to be a basis of a subspace of the dual space

Published on 18 Jan 2021 - 19:58

23

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Dimension of a subspace of $K^S$

Published on 19 Jan 2021 - 17:53

49

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Defining a linear functional on a subspace of the dual space

Published on 21 Jan 2021 - 20:24

259

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Is there any meaning or basis-free description for coevaluation in FDVect?

Published on 22 Jan 2021 - 0:08

279

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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 25 Mar 2026 - 20:50

57

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Given $f \in V^$ and $\mathscr A : V \to V$ a linear map, show that $f,f \circ \mathscr A,\dots,f \circ \mathscr A^{n-1}$ is a basis for $V^$

Published on 26 Mar 2026 - 21:14

501

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Proving that the induced connection on the dual bundle is indeed a connection

Published on 29 Mar 2026 - 20:06

161

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Pure State Definition Confusion

Published on 25 Jan 2021 - 15:11

41

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Rank of a tensor

Published on 25 Jan 2021 - 18:48

70

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Dual operator on $C([0,2 \pi])$

Published on 28 Jan 2021 - 16:01

132

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How is the dual space generated from the linear forms?

Published on 30 Jan 2021 - 0:32

List Question

Example for topological dual spaces

Coordinates of a functional in dual space with one qiven coordinate.

Proof that the canonical mapping of $V$ into $V^{**}$ is not bijective

Prove that the map $A \mapsto (B \mapsto \operatorname{trace}(AB))$ is an isomorphism $\operatorname{Mat}_{n,m}(K) \to \operatorname{Mat}_{m,n}(K)^*$

Condition for a finite sequence to be a basis of a subspace of the dual space

Dimension of a subspace of $K^S$

Defining a linear functional on a subspace of the dual space

Is there any meaning or basis-free description for coevaluation in FDVect?

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

Given $f \in V^$ and $\mathscr A : V \to V$ a linear map, show that $f,f \circ \mathscr A,\dots,f \circ \mathscr A^{n-1}$ is a basis for $V^$

Proving that the induced connection on the dual bundle is indeed a connection

Pure State Definition Confusion

Rank of a tensor

Dual operator on $C([0,2 \pi])$

How is the dual space generated from the linear forms?

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