List questions from vector-space-isomorphism

Published on 06 Nov 2015 - 0:43

74

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Using a basis of Polynomials in Pn-1 to prove a modified Riemann Sum Formula

Published on 05 Mar 2026 - 7:44

40

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Is the function $\alpha$ an isomorphism?

Published on 11 Nov 2015 - 23:04

113

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How would you prove that the kernel of a linear mapping $\theta\colon V \rightarrow W$ is a subspace of $V$?

Published on 25 Mar 2026 - 17:15

693

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Why are vectors and one-forms treated as equal in Euclidean space?

Published on 12 Mar 2026 - 4:49

177

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If $X/F$ is separable, must $X/F$ isomorphic to $F$?

Published on 05 Dec 2015 - 6:20

138

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Why is $\mathbb{R}^2$ not a vector subspace of $\mathbb{R}^3$?

Published on 22 Feb 2026 - 21:53

101

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What are we allowed to do when we know that two metric spaces are isometrically isomorphic?

Published on 08 Dec 2015 - 15:36

37

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If $N$ is a subset of $M$, show that $Lip_0(N)$ is linearly isomorphic to $Lip_0(\bar{N})$

Published on 11 Dec 2015 - 8:06

66

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A Problem about Vector Spaces and Linear Maps

Published on 12 Dec 2015 - 18:22

2.2k

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Determine whether the transformation is an isomorphism

Published on 16 Dec 2015 - 18:40

2.5k

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Isometric isomorphism from $\ell^1$ to $c^*$

Published on 17 Dec 2015 - 23:36

134

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Are $\Bbb C^4 $and polynomials of degree at most five isomorphic vector spaces?

Published on 21 Dec 2015 - 18:43

1.2k

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is linear independence preserved under isomorphism?

Published on 21 Dec 2015 - 19:06

619

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Isomorphism between two subspaces of two spaces of different dimensions

Published on 25 Dec 2015 - 0:01

List Question

Problem on Homomorphism, isomorphism, and dot product.

Using a basis of Polynomials in Pn-1 to prove a modified Riemann Sum Formula

Is the function $\alpha$ an isomorphism?

How would you prove that the kernel of a linear mapping $\theta\colon V \rightarrow W$ is a subspace of $V$?

Why are vectors and one-forms treated as equal in Euclidean space?

If $X/F$ is separable, must $X/F$ isomorphic to $F$?

Why is $\mathbb{R}^2$ not a vector subspace of $\mathbb{R}^3$?

What are we allowed to do when we know that two metric spaces are isometrically isomorphic?

If $N$ is a subset of $M$, show that $Lip_0(N)$ is linearly isomorphic to $Lip_0(\bar{N})$

A Problem about Vector Spaces and Linear Maps

Determine whether the transformation is an isomorphism

Isometric isomorphism from $\ell^1$ to $c^*$

Are $\Bbb C^4 $and polynomials of degree at most five isomorphic vector spaces?

is linear independence preserved under isomorphism?

Isomorphism between two subspaces of two spaces of different dimensions

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