Question

Let $H$ be $H_i$ 's are vector subspaces of dimension $n$. If $\bigcup\limits_{i=1}^r H_i$ contains $H$, then $H = H_i$ for some $i$.

score 28 · Answer 1 · 2018-02-27 18:04:15

Let $H$ be $H_i$ 's are vector subspaces of dimension $n$. If $\bigcup\limits_{i=1}^r H_i$ contains $H$, then $H = H_i$ for some $i$.

score 4.8k · Answer 2 · 2026-03-25 14:25:53

4.8k

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What subspace of $3 \times 3$ matrices is spanned by a given set?

Published on 25 Mar 2026 - 14:25

score 1.2k · Answer 3 · 2018-02-28 02:14:53

1.2k

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Suppose $V$ is finite-dimensional with dim $V>1$ and $T\in \mathscr L (V)$. Prove that $\{p(T):p\in \mathscr P(\Bbb F)\}\neq \mathscr L(V)$.

Published on 28 Feb 2018 - 2:14

score 459 · Answer 4 · 2026-03-24 22:13:59

459

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Example of infinite dimensional linear spaces where the space is equal to its dual.

Published on 24 Mar 2026 - 22:13

score 41 · Answer 5 · 2018-02-28 04:41:12

41

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Parallels between subspaces of vector spaces, and closed sets: result of formal logic?

Published on 28 Feb 2018 - 4:41

score 986 · Answer 6 · 2018-02-28 10:14:43

986

Views

Recommended Book after Finite-Dimensional Vector Spaces by Halmos

Published on 28 Feb 2018 - 10:14

score 547 · Answer 7 · 2018-02-28 13:44:45

547

Views

Is there a semi-norm that respects matrix similitary?

Published on 28 Feb 2018 - 13:44

score 105 · Answer 8 · 2026-03-19 18:33:49

105

Views

Find the number of $n-1$ dimensional subspaces $V_2$ such that $V_1+V_2=V$ where $\dim V_1=1$

Published on 19 Mar 2026 - 18:33

score 54 · Answer 9 · 2018-02-28 15:03:37

54

Views

Prove that $ E \cap (F + (E \cap G)) = (E \cap F) + (E \cap G)$

Published on 28 Feb 2018 - 15:03

score 1.1k · Answer 10 · 2018-03-01 06:20:04

1.1k

Views

Find the dimension of the vector space of 7×7 matrices with zero trace

Published on 01 Mar 2018 - 6:20

score 141 · Answer 11 · 2026-03-26 04:22:40

141

Views

Can we prove that a set of polynomials is a basis for a vector space using induction?

Published on 26 Mar 2026 - 4:22

score 749 · Answer 12 · 2018-03-01 21:40:09

749

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Prove that set is a basis for a column space

Published on 01 Mar 2018 - 21:40

score 1.4k · Answer 13 · 2026-03-23 06:12:27

1.4k

Views

Legendre Polynomials form a Basis

Published on 23 Mar 2026 - 6:12

score 844 · Answer 14 · 2018-03-02 07:24:45

844

Views

Determining if a set of complex numbers spans

Published on 02 Mar 2018 - 7:24

score 242 · Answer 15 · 2026-03-24 22:01:25

242

Views

Volume of a paralellepiped

Published on 24 Mar 2026 - 22:01

List Question

Let $H$ be $H_i$ 's are vector subspaces of dimension $n$. If $\bigcup\limits_{i=1}^r H_i$ contains $H$, then $H = H_i$ for some $i$.

What subspace of $3 \times 3$ matrices is spanned by a given set?

Suppose $V$ is finite-dimensional with dim $V>1$ and $T\in \mathscr L (V)$. Prove that $\{p(T):p\in \mathscr P(\Bbb F)\}\neq \mathscr L(V)$.

Example of infinite dimensional linear spaces where the space is equal to its dual.

Parallels between subspaces of vector spaces, and closed sets: result of formal logic?

Recommended Book after Finite-Dimensional Vector Spaces by Halmos

Is there a semi-norm that respects matrix similitary?

Find the number of $n-1$ dimensional subspaces $V_2$ such that $V_1+V_2=V$ where $\dim V_1=1$

Prove that $ E \cap (F + (E \cap G)) = (E \cap F) + (E \cap G)$

Find the dimension of the vector space of 7×7 matrices with zero trace

Can we prove that a set of polynomials is a basis for a vector space using induction?

Prove that set is a basis for a column space

Legendre Polynomials form a Basis

Determining if a set of complex numbers spans

Volume of a paralellepiped

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