List questions from vector-space-isomorphism

Published on 24 Dec 2020 - 19:25

927

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Given two vector spaces $V,W$ with finite dimension,show that they are isomorphic if and only if $\text{dim(V)}=\text{dim(W)}$.

Published on 28 Dec 2020 - 17:02

332

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Show that $\mathbb F^{ \;m \times n}$ is isomorphic to $\mathbb F^{m n}$,where $\mathbb F$ is a field.

Published on 29 Dec 2020 - 9:19

100

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A question about the relation between linear transformations and their representing matrices

Published on 29 Dec 2020 - 23:15

156

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Finding an isomorphism between spans

Published on 30 Dec 2020 - 13:25

44

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$C([0,1], \ell_p)$ has a copy of $\ell_q$?

Published on 03 Jan 2021 - 1:33

560

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Can every isomorphism between a vector space and its dual be written as a non-degenerate bilinear form?

Published on 05 Jan 2021 - 16:49

225

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Inverse function theorem and tangent space differentials

Published on 25 Mar 2026 - 23:35

45

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Space of functions from [0,1] to IR and from IR to IR

Published on 12 Jan 2021 - 23:54

160

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Showing that a linear transformation is an isomorphism.

Published on 26 Jan 2021 - 14:40

48

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Connection between vector space isomorphisms and dimensions

Published on 27 Jan 2021 - 18:25

134

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Isomorphism map between $\frac{\mathbb{Z}_3[x]}{(x^2+x+2)}$ and $ \frac{\mathbb{Z}_3[x]}{(x^2 + 1)} $

Published on 04 Feb 2021 - 13:47

46

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values of determinants?

Published on 07 Feb 2021 - 18:42

45

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Weird condition implies isomorphism between vector spaces?

Published on 24 Feb 2021 - 14:48

27

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Isomorphism and Invertible Matrices

Published on 10 Mar 2021 - 8:53

List Question

Number of one to one linear transformations

Given two vector spaces $V,W$ with finite dimension,show that they are isomorphic if and only if $\text{dim(V)}=\text{dim(W)}$.

Show that $\mathbb F^{ \;m \times n}$ is isomorphic to $\mathbb F^{m n}$,where $\mathbb F$ is a field.

A question about the relation between linear transformations and their representing matrices

Finding an isomorphism between spans

$C([0,1], \ell_p)$ has a copy of $\ell_q$?

Can every isomorphism between a vector space and its dual be written as a non-degenerate bilinear form?

Inverse function theorem and tangent space differentials

Space of functions from [0,1] to IR and from IR to IR

Showing that a linear transformation is an isomorphism.

Connection between vector space isomorphisms and dimensions

Isomorphism map between $\frac{\mathbb{Z}_3[x]}{(x^2+x+2)}$ and $ \frac{\mathbb{Z}_3[x]}{(x^2 + 1)} $

values of determinants?

Weird condition implies isomorphism between vector spaces?

Isomorphism and Invertible Matrices

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