Question

Proving $(V\oplus W)^\cong V^\oplus W^*$

score 76 · Answer 1 · 2020-01-15 17:36:06

76

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Proving $(V\oplus W)^\cong V^\oplus W^*$

Published on 15 Jan 2020 - 17:36

score 54 · Answer 2 · 2020-01-18 20:44:14

54

Views

Showing a matrix is 1-1

Published on 18 Jan 2020 - 20:44

score 444 · Answer 3 · 2020-01-22 14:53:45

444

Views

What does is mean when a composition of two functions is an isomorphism?

Published on 22 Jan 2020 - 14:53

score 48 · Answer 4 · 2020-01-24 20:53:07

48

Views

$T(A)=BA$ for every $A\in \mathbb{R}^{n\times n}$ prove\disprove that if $T$ is not isomorphism then $\det(B)=0$

Published on 24 Jan 2020 - 20:53

score 126 · Answer 5 · 2020-01-26 12:44:13

126

Views

determine if the pair of vector spaces is isomorphic

Published on 26 Jan 2020 - 12:44

score 986 · Answer 6 · 2020-02-08 18:03:21

986

Views

prove: For any finite-dimension vector space $V$ with ordered basis $\beta$, $\phi_\beta$ is an isomorphism.

Published on 08 Feb 2020 - 18:03

score 69 · Answer 7 · 2020-02-08 21:14:05

69

Views

$T_{\varepsilon} = Id + \varepsilon T$ is an isomorphism for some $\varepsilon$

Published on 08 Feb 2020 - 21:14

score 1.4k · Answer 8 · 2020-02-12 06:23:38

1.4k

Views

Let $T: V \rightarrow W$ and $S: W \rightarrow Z$ be linear maps. If $S\circ T$ is an isomorphism, are $S$ and $T$ isomorphisms?

Published on 12 Feb 2020 - 6:23

score 65 · Answer 9 · 2020-02-12 18:44:04

65

Views

Concept check: Let V and W be subspaces, and $T: V \rightarrow W$ be linear.

Published on 12 Feb 2020 - 18:44

score 129 · Answer 10 · 2020-02-16 21:37:22

129

Views

Definition of Homomorphism of $I$-Graded Vector Spaces

Published on 16 Feb 2020 - 21:37

score 2.4k · Answer 11 · 2020-02-21 03:46:02

2.4k

Views

Let $V$ and $W$ be finite-dimensional vector spaces. Prove that $V$ and $W$ are isomorphic if and only if $\dim V = \dim W$.

Published on 21 Feb 2020 - 3:46

score 502 · Answer 12 · 2020-03-04 00:10:07

502

Views

Trying to understand change of basis

Published on 04 Mar 2020 - 0:10

score 37 · Answer 13 · 2020-03-06 00:42:57

37

Views

Direct sum of HIlbert spaces isomorphic to...

Published on 06 Mar 2020 - 0:42

score 118 · Answer 14 · 2020-03-08 08:16:22

118

Views

What is the connection between the fundamental subspaces and finite-dimensional vector spaces being isomorphic to $\mathbb R^n$

Published on 08 Mar 2020 - 8:16

score 264 · Answer 15 · 2020-03-09 15:54:27

264

Views

Detail in the Fredholm alternative: necessity to prove $\operatorname{codim}\operatorname{Im}(I-K) = \operatorname{dim}\operatorname{Ker}(I-K)$

Published on 09 Mar 2020 - 15:54

List Question

Proving $(V\oplus W)^\cong V^\oplus W^*$

Showing a matrix is 1-1

What does is mean when a composition of two functions is an isomorphism?

$T(A)=BA$ for every $A\in \mathbb{R}^{n\times n}$ prove\disprove that if $T$ is not isomorphism then $\det(B)=0$

determine if the pair of vector spaces is isomorphic

prove: For any finite-dimension vector space $V$ with ordered basis $\beta$, $\phi_\beta$ is an isomorphism.

$T_{\varepsilon} = Id + \varepsilon T$ is an isomorphism for some $\varepsilon$

Let $T: V \rightarrow W$ and $S: W \rightarrow Z$ be linear maps. If $S\circ T$ is an isomorphism, are $S$ and $T$ isomorphisms?

Concept check: Let V and W be subspaces, and $T: V \rightarrow W$ be linear.

Definition of Homomorphism of $I$-Graded Vector Spaces

Let $V$ and $W$ be finite-dimensional vector spaces. Prove that $V$ and $W$ are isomorphic if and only if $\dim V = \dim W$.

Trying to understand change of basis

Direct sum of HIlbert spaces isomorphic to...

What is the connection between the fundamental subspaces and finite-dimensional vector spaces being isomorphic to $\mathbb R^n$

Detail in the Fredholm alternative: necessity to prove $\operatorname{codim}\operatorname{Im}(I-K) = \operatorname{dim}\operatorname{Ker}(I-K)$

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