Question

Why are $T^k(V)$ and $V^* \otimes... \otimes V^*$ just isomorphic?

score 49 · Answer 1 · 2026-03-20 15:09:40

49

Views

Why are $T^k(V)$ and $V^* \otimes... \otimes V^*$ just isomorphic?

Published on 20 Mar 2026 - 15:09

score 1.7k · Answer 2 · 2026-03-20 06:40:02

1.7k

Views

Show $T$ is an invertible linear map iff $\operatorname{rank} T = \dim V$

Published on 20 Mar 2026 - 6:40

score 70 · Answer 3 · 2026-03-20 05:13:05

Let $V$ be a finite dimensional real vector space. If $S,T∈L(V,V)$ prove that $ST$ and $TS$ have the same eigenvalues whenever $T$ is an isomorphism

score 46 · Answer 4 · 2026-03-20 15:03:11

46

Views

Prove that $\Bbb R^n$ and $\mathcal L(\Bbb R,\Bbb R^n)$ are isomorphic.

Published on 20 Mar 2026 - 15:03

score 100 · Answer 5 · 2026-03-20 09:13:50

100

Views

How can vector space $V\subsetneq W$ but $V\cong W$, where $V$ and $W$ don't have finite dimensions?

Published on 20 Mar 2026 - 9:13

score 1.2k · Answer 6 · 2026-03-19 23:04:45

1.2k

Views

Prove that if $f$ is a diffeomorphism than its differential $D_{f}$ is an isomorphism

Published on 19 Mar 2026 - 23:04

score 379 · Answer 7 · 2026-03-25 04:35:38

379

Views

Invariants between two isomorphic vector spaces

Published on 25 Mar 2026 - 4:35

score 459 · Answer 8 · 2019-03-27 19:17:26

459

Views

Why does $\mathscr{P}_2$ being isomorphic to $R^3$ imply that a constantwise addition of objects in $\mathscr{P}_2$ is an inner product?

Published on 27 Mar 2019 - 19:17

score 234 · Answer 9 · 2026-03-20 00:02:40

234

Views

Sheldon Axler 3.117: How to understand the proof

Published on 20 Mar 2026 - 0:02

score 497 · Answer 10 · 2026-03-20 13:01:27

497

Views

Proving entire sequence space and the subspace of sequences with finitely many non-zero entries are not isomorphic

Published on 20 Mar 2026 - 13:01

score 159 · Answer 11 · 2026-03-20 13:40:35

159

Views

Show that $Γ$ is isomorphic to $L(V/W,V')$

Published on 20 Mar 2026 - 13:40

score 55 · Answer 12 · 2026-03-20 00:00:13

55

Views

Quotient of quotients in finite dimensional vector spaces

Published on 20 Mar 2026 - 0:00

score 64 · Answer 13 · 2026-03-19 07:57:33

64

Views

Prove that there exists an ordered basis $\gamma$ for which $[T^*]_\gamma$ has a column of $0$s.

Published on 19 Mar 2026 - 7:57

score 616 · Answer 14 · 2026-03-20 13:53:06

616

Views

Are any two isomorphic normed linear spaces homeomorphic?

Published on 20 Mar 2026 - 13:53

score 414 · Answer 15 · 2026-03-19 12:13:24

414

Views

Are two submodules (where one is contained in the other) isomorphic if their quotientmodules are isomorphic?

Published on 19 Mar 2026 - 12:13

List Question

Why are $T^k(V)$ and $V^* \otimes... \otimes V^*$ just isomorphic?

Show $T$ is an invertible linear map iff $\operatorname{rank} T = \dim V$

Let $V$ be a finite dimensional real vector space. If $S,T∈L(V,V)$ prove that $ST$ and $TS$ have the same eigenvalues whenever $T$ is an isomorphism

Prove that $\Bbb R^n$ and $\mathcal L(\Bbb R,\Bbb R^n)$ are isomorphic.

How can vector space $V\subsetneq W$ but $V\cong W$, where $V$ and $W$ don't have finite dimensions?

Prove that if $f$ is a diffeomorphism than its differential $D_{f}$ is an isomorphism

Invariants between two isomorphic vector spaces

Why does $\mathscr{P}_2$ being isomorphic to $R^3$ imply that a constantwise addition of objects in $\mathscr{P}_2$ is an inner product?

Sheldon Axler 3.117: How to understand the proof

Proving entire sequence space and the subspace of sequences with finitely many non-zero entries are not isomorphic

Show that $Γ$ is isomorphic to $L(V/W,V')$

Quotient of quotients in finite dimensional vector spaces

Prove that there exists an ordered basis $\gamma$ for which $[T^*]_\gamma$ has a column of $0$s.

Are any two isomorphic normed linear spaces homeomorphic?

Are two submodules (where one is contained in the other) isomorphic if their quotientmodules are isomorphic?

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