Question

Three space property

score 169 · Answer 1 · 2026-03-22 20:49:56

169

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Three space property

Published on 22 Mar 2026 - 20:49

score 201 · Answer 2 · 2018-11-16 09:40:15

201

Views

Suppose that $(u_1,\ldots, u_m, v_1, \ldots, v_n)$ is linearly independent. Prove that $W_1 ∩ W_2 = \{0\}$.

Published on 16 Nov 2018 - 9:40

score 235 · Answer 3 · 2018-11-25 17:50:13

235

Views

An incomplete inner product space with an orthonormal basis that is not a Hamel basis

Published on 25 Nov 2018 - 17:50

score 39 · Answer 4 · 2018-12-13 21:05:25

39

Views

Let $v \in \operatorname{Im}(p)$. Compute $p(v)$.

Published on 13 Dec 2018 - 21:05

score 210 · Answer 5 · 2018-12-25 11:45:38

210

Views

$\{x_1,...,x_n\}$ a basis of $V_1$; SHOW THAT there is a unique linear transformation $f:V_1\to V_2$ such that $f(x_1)=y_i$

Published on 25 Dec 2018 - 11:45

score 1.7k · Answer 6 · 2018-12-28 17:56:32

1.7k

Views

how to prove that a linear transformation maps every basis to the basis of the coordinate space

Published on 28 Dec 2018 - 17:56

score 1.8k · Answer 7 · 2019-01-06 18:42:26

1.8k

Views

What is the general method of expressing a basis in terms of another basis of a vector space?

Published on 06 Jan 2019 - 18:42

score 319 · Answer 8 · 2019-01-08 10:34:04

319

Views

Find a linear map knowing its image and kernel

Published on 08 Jan 2019 - 10:34

score 71 · Answer 9 · 2019-01-11 15:13:23

71

Views

How to find a basis of $\Bbb R(t)$ over $\Bbb R$?

Published on 11 Jan 2019 - 15:13

score 51 · Answer 10 · 2019-01-20 18:13:20

51

Views

Why is $ (a, b) = 0 $ for distinct $ a, b \in A $, the Hamel basis of vector space $ \mathbb{R} $ over $ \mathbb{Q} $?

Published on 20 Jan 2019 - 18:13

score 201 · Answer 11 · 2019-02-08 18:45:10

201

Views

Existence of orthogonal Hamel basis for infinite dimensional vector space.

Published on 08 Feb 2019 - 18:45

score 176 · Answer 12 · 2019-03-02 08:17:22

176

Views

Is it true? $\dim(U+W)=\dim(U\cap W)+1$ implies $U\subseteq W$

Published on 02 Mar 2019 - 8:17

score 108 · Answer 13 · 2019-03-05 09:46:51

108

Views

Does the statement "Every short exact sequence of vector spaces splits" imply the axiom of choice?

Published on 05 Mar 2019 - 9:46

score 100 · Answer 14 · 2019-03-08 21:08:23

100

Views

Does the existence of a linear functional on $C_0^\infty(\mathbb R)$ which is not a distribution require the axiom of choice?

Published on 08 Mar 2019 - 21:08

score 361 · Answer 15 · 2019-03-28 15:59:05

361

Views

Will the span of vectors {(1,0,0,0,0),(0,1,0,0,0)} form a subspace/basis in the set of fields of dimension 5?

Published on 28 Mar 2019 - 15:59

List Question

Three space property

Suppose that $(u_1,\ldots, u_m, v_1, \ldots, v_n)$ is linearly independent. Prove that $W_1 ∩ W_2 = \{0\}$.

An incomplete inner product space with an orthonormal basis that is not a Hamel basis

Let $v \in \operatorname{Im}(p)$. Compute $p(v)$.

$\{x_1,...,x_n\}$ a basis of $V_1$; SHOW THAT there is a unique linear transformation $f:V_1\to V_2$ such that $f(x_1)=y_i$

how to prove that a linear transformation maps every basis to the basis of the coordinate space

What is the general method of expressing a basis in terms of another basis of a vector space?

Find a linear map knowing its image and kernel

How to find a basis of $\Bbb R(t)$ over $\Bbb R$?

Why is $ (a, b) = 0 $ for distinct $ a, b \in A $, the Hamel basis of vector space $ \mathbb{R} $ over $ \mathbb{Q} $?

Existence of orthogonal Hamel basis for infinite dimensional vector space.

Is it true? $\dim(U+W)=\dim(U\cap W)+1$ implies $U\subseteq W$

Does the statement "Every short exact sequence of vector spaces splits" imply the axiom of choice?

Does the existence of a linear functional on $C_0^\infty(\mathbb R)$ which is not a distribution require the axiom of choice?

Will the span of vectors {(1,0,0,0,0),(0,1,0,0,0)} form a subspace/basis in the set of fields of dimension 5?

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