List questions from hamel-basis

Published on 14 Feb 2021 - 20:22

170

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Why is it important that every (infinite) dimensional vector space has a (hamel) basis?

Published on 24 Feb 2021 - 12:27

38

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Checking if given set forms basis for $P_3(\mathbb{R})$

Published on 26 Feb 2021 - 6:33

209

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Prove that if there exists an infinite linearly independent subset E, of a vector space V, then V is infinite dimensional.

Published on 25 Mar 2026 - 19:06

138

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Basis of $V=\{a\cdot(1,2,3)^T\}$

Published on 17 Mar 2021 - 9:40

81

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Is the direct sum decomposition of formal power series provable without choice?

Published on 18 Mar 2021 - 4:53

583

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If $\beta$ is a basis of $V$ then does that mean that $V=span{\beta}$?

Published on 20 Mar 2021 - 7:25

65

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Tying Span, Basis, Linear Independence, Dimension Together

Published on 28 Mar 2021 - 5:04

158

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Finding basis and explain why the basis have found is a basis

Published on 18 Apr 2021 - 10:32

120

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Clarification Regarding Banach space and Baire Category Theorem

Published on 04 May 2021 - 5:10

735

Views

Is the span closed?

Published on 14 May 2021 - 20:43

224

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For any vector space with a basis, does there exist a choice of inner product w.r.t. which the basis is orthonormal?

Published on 06 Jul 2021 - 12:33

877

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Finding the basis of ker(T) and im(T)

Published on 19 Jul 2021 - 7:46

142

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Basis of a completion of a vector space

Published on 25 Mar 2026 - 13:59

154

Views

How to show that the reciprocal set is also a basis of $\mathbb{R}^3$

Published on 28 Aug 2021 - 17:54

List Question

Hamel basis for $\mathbb{R}_{\geq 0}$ as a vector space over $\mathbb{F}_2$

Why is it important that every (infinite) dimensional vector space has a (hamel) basis?

Checking if given set forms basis for $P_3(\mathbb{R})$

Prove that if there exists an infinite linearly independent subset E, of a vector space V, then V is infinite dimensional.

Basis of $V=\{a\cdot(1,2,3)^T\}$

Is the direct sum decomposition of formal power series provable without choice?

If $\beta$ is a basis of $V$ then does that mean that $V=span{\beta}$?

Tying Span, Basis, Linear Independence, Dimension Together

Finding basis and explain why the basis have found is a basis

Clarification Regarding Banach space and Baire Category Theorem

Is the span closed?

For any vector space with a basis, does there exist a choice of inner product w.r.t. which the basis is orthonormal?

Finding the basis of ker(T) and im(T)

Basis of a completion of a vector space

How to show that the reciprocal set is also a basis of $\mathbb{R}^3$

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