List questions from vector-space-isomorphism

Published on 04 Jun 2021 - 7:05

384

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Can $L^p(\mathbb{R})$ and $L^p[0,1]$ be isomorphic?

Published on 23 Jun 2021 - 0:19

369

Views

Natural isomorphism in linear algebra: is the naturalness asymmetric?

Published on 23 Jun 2021 - 8:13

71

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Proving isomorphism between two spaces of the linear transformations

Published on 02 Jul 2021 - 0:21

235

Views

Isomorphism between $V^* \otimes V$ and $\operatorname{End} V$

Published on 11 Jul 2021 - 12:12

2.7k

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Show that $V$ and $\mathcal{L} (\mathbb{F},V)$ are isomorphic vector spaces.

Published on 11 Jul 2021 - 23:29

207

Views

Can an arbitrary vector space over $\mathbb{F}$ be written as $\mathbb{F}^X$ for some set $X$?

Published on 29 Jul 2021 - 10:37

75

Views

Prove that Diag$_n(\mathbb{R})$ is isomorphic to $\mathbb{R}^n$

Published on 07 Aug 2021 - 1:34

78

Views

Doubt about $\mathbb C\left[ X\times Y \right]$ and $\mathbb C\left[ X\right]\times\mathbb C\left[ Y\right]$ being isomorphic.

Published on 08 Aug 2021 - 15:05

165

Views

Matrix spaces A,B with the same dimension implying B=QAP?

Published on 22 Aug 2021 - 3:41

92

Views

Showing a linear transformation $T\colon V^{*}\to\mathbb R^{m}$ is surjective

Published on 22 Aug 2021 - 10:19

26

Views

Proving that an isomorphism from a vector space $X$ to $X'$ using symmetric bilinear forms is onto

Published on 25 Aug 2021 - 15:29

163

Views

two norms are equivalent

Published on 31 Aug 2021 - 3:51

65

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How should I read/interpret this notation?

Published on 03 Sep 2021 - 12:27

89

Views

Why is dimension an invariant between finite-dimensional isomorphic vector spaces?

Published on 05 Sep 2021 - 13:16

List Question

Isomorphism between dual of quotient and annihilator

Can $L^p(\mathbb{R})$ and $L^p[0,1]$ be isomorphic?

Natural isomorphism in linear algebra: is the naturalness asymmetric?

Proving isomorphism between two spaces of the linear transformations

Isomorphism between $V^* \otimes V$ and $\operatorname{End} V$

Show that $V$ and $\mathcal{L} (\mathbb{F},V)$ are isomorphic vector spaces.

Can an arbitrary vector space over $\mathbb{F}$ be written as $\mathbb{F}^X$ for some set $X$?

Prove that Diag$_n(\mathbb{R})$ is isomorphic to $\mathbb{R}^n$

Doubt about $\mathbb C\left[ X\times Y \right]$ and $\mathbb C\left[ X\right]\times\mathbb C\left[ Y\right]$ being isomorphic.

Matrix spaces A,B with the same dimension implying B=QAP?

Showing a linear transformation $T\colon V^{*}\to\mathbb R^{m}$ is surjective

Proving that an isomorphism from a vector space $X$ to $X'$ using symmetric bilinear forms is onto

two norms are equivalent

How should I read/interpret this notation?

Why is dimension an invariant between finite-dimensional isomorphic vector spaces?

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