Question

$X, Y$ subspaces of $V$, $\dim(X) \geq \dim(Y) \implies \exists f$ linear s.t. $f(X)=Y$

score 111 · Answer 1 · 2026-03-21 19:46:26

111

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$X, Y$ subspaces of $V$, $\dim(X) \geq \dim(Y) \implies \exists f$ linear s.t. $f(X)=Y$

Published on 21 Mar 2026 - 19:46

score 58 · Answer 2 · 2026-03-21 16:37:35

58

Views

A question on a result.

Published on 21 Mar 2026 - 16:37

score 76 · Answer 3 · 2026-03-22 00:06:53

76

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If $l$ is an integer such that $k \le l \le m$, show that there exists subspace $X$ of $V$ such that $U \subseteq X \subseteq W$ and $\dim(X)=l$.

Published on 22 Mar 2026 - 0:06

score 30 · Answer 4 · 2026-03-22 05:09:59

30

Views

Finding the dimension of the Kernel $\mathbb{R}^{3*2} \rightarrow \mathbb{R}_4[x]$

Published on 22 Mar 2026 - 5:09

score 43 · Answer 5 · 2026-03-22 00:49:30

43

Views

Feedback to Basis and Dimension of $A:= \{x\in\mathbb{R}^4 | x_2 + 3x_3= 0, x_1=x_2\}$

Published on 22 Mar 2026 - 0:49

score 1.8k · Answer 6 · 2026-03-21 23:12:39

1.8k

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Let $T : U → V$ and $S : V → W$ be linear transformations. How is $\operatorname{rank}(ST)$ related to $\operatorname{rank}(T)$?

Published on 21 Mar 2026 - 23:12

score 72 · Answer 7 · 2026-03-21 21:32:40

72

Views

Proving equality of column space to field

Published on 21 Mar 2026 - 21:32

score 214 · Answer 8 · 2026-03-21 16:45:02

214

Views

Dimension of quasi-affine variety

Published on 21 Mar 2026 - 16:45

score 97 · Answer 9 · 2026-03-21 18:02:03

97

Views

Generalizing a previous result on height of irreducible polynomials (special case of Krull's Principal Ideal Theorem)

Published on 21 Mar 2026 - 18:02

score 69 · Answer 10 · 2026-03-22 15:37:05

69

Views

What does it mean A contains a field k mapping isomorphically onto the residue field A/m in Atiyah Macdonald 11.21?

Published on 22 Mar 2026 - 15:37

score 294 · Answer 11 · 2021-07-21 09:57:49

294

Views

Understanding Matousek's proof of Equiangular lines

Published on 21 Jul 2021 - 9:57

score 100 · Answer 12 · 2021-08-28 17:32:09

100

Views

Subspaces in linear algebra - Matrix

Published on 28 Aug 2021 - 17:32

score 392 · Answer 13 · 2021-10-04 19:16:27

392

Views

$\mathbb C[y_1,\cdots, y_\ell]/I,$ where $I$ is generated by the relation $\sum_j(-1)^je_j h_{m-j}$ of symmetric polynomials, is $\ell!$-dimensional

Published on 04 Oct 2021 - 19:16

score 171 · Answer 14 · 2021-10-09 07:28:16

171

Views

Gelfand-Kirillov dimension of a finite extension.

Published on 09 Oct 2021 - 7:28

score 119 · Answer 15 · 2021-10-10 13:11:07

119

Views

Dimension of Quot scheme

Published on 10 Oct 2021 - 13:11

List Question

$X, Y$ subspaces of $V$, $\dim(X) \geq \dim(Y) \implies \exists f$ linear s.t. $f(X)=Y$

A question on a result.

If $l$ is an integer such that $k \le l \le m$, show that there exists subspace $X$ of $V$ such that $U \subseteq X \subseteq W$ and $\dim(X)=l$.

Finding the dimension of the Kernel $\mathbb{R}^{3*2} \rightarrow \mathbb{R}_4[x]$

Feedback to Basis and Dimension of $A:= \{x\in\mathbb{R}^4 | x_2 + 3x_3= 0, x_1=x_2\}$

Let $T : U → V$ and $S : V → W$ be linear transformations. How is $\operatorname{rank}(ST)$ related to $\operatorname{rank}(T)$?

Proving equality of column space to field

Dimension of quasi-affine variety

Generalizing a previous result on height of irreducible polynomials (special case of Krull's Principal Ideal Theorem)

What does it mean A contains a field k mapping isomorphically onto the residue field A/m in Atiyah Macdonald 11.21?

Understanding Matousek's proof of Equiangular lines

Subspaces in linear algebra - Matrix

$\mathbb C[y_1,\cdots, y_\ell]/I,$ where $I$ is generated by the relation $\sum_j(-1)^je_j h_{m-j}$ of symmetric polynomials, is $\ell!$-dimensional

Gelfand-Kirillov dimension of a finite extension.

Dimension of Quot scheme

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