Question

Isomorphism by restricting surjective linear mapping between finite dimensional spaces, and quotient space by null space

score 1.3k · Answer 1 · 2020-06-16 16:03:35

1.3k

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Isomorphism by restricting surjective linear mapping between finite dimensional spaces, and quotient space by null space

Published on 16 Jun 2020 - 16:03

score 88 · Answer 2 · 2020-06-19 23:03:24

88

Views

$L_p(\mu,X)$ is isometrically isomorphic to $\ell_p(X)$

Published on 19 Jun 2020 - 23:03

score 454 · Answer 3 · 2020-06-23 17:05:43

454

Views

Show that $\Bbb{F}^{m×n}$ is isomorphic to $\Bbb{F}^{mn}$.

Published on 23 Jun 2020 - 17:05

score 11.6k · Answer 4 · 2020-06-24 11:17:48

11.6k

Views

Let $V$ and $W$ be finite dimensional vector spaces over the field $F$. Prove that $V$ is isomorphic to $W$ iff $dimV=dimW$.

Published on 24 Jun 2020 - 11:17

score 102 · Answer 5 · 2020-06-27 17:35:18

102

Views

About the existence of an isomorphism of algebras between the algebras of $\mathcal{C}^0$ and $\mathcal{C}^1$ functions from $[0, 1]$ to $\mathbb{R}$

Published on 27 Jun 2020 - 17:35

score 49 · Answer 6 · 2020-07-01 23:00:23

49

Views

Do theorems concerning isomorphisms that apply to Vector spaces also apply to subspaces?

Published on 01 Jul 2020 - 23:00

score 67 · Answer 7 · 2020-07-07 14:15:24

67

Views

If $u$ is an isomorphism of $E$ into $F$, prove that to every $n$ there is $m$ such that $u^{-1}(F_n) \subset E_m$

Published on 07 Jul 2020 - 14:15

score 63 · Answer 8 · 2020-07-16 01:09:44

63

Views

Isomorphism between $\bigwedge^2\mathbb R^3$ and the dual of $\mathfrak{so}(3)$

Published on 16 Jul 2020 - 1:09

score 56 · Answer 9 · 2020-07-17 11:53:43

56

Views

Do properties in linear algebra proved by using matrix transformations hold true irrespective of the choice of the bases for the vector spaces?

Published on 17 Jul 2020 - 11:53

score 109 · Answer 10 · 2020-07-18 16:18:38

109

Views

Question on showing invertibility of function $\Phi: \mathcal{L}(V,W) \to M_{m \times n}(F)$ in regards to establishing an isomorphism.

Published on 18 Jul 2020 - 16:18

score 114 · Answer 11 · 2020-07-21 20:05:24

114

Views

Homomorphic Image of ideal in Lie algebras

Published on 21 Jul 2020 - 20:05

score 197 · Answer 12 · 2020-07-24 02:10:01

197

Views

Proving a linear map is surjective

Published on 24 Jul 2020 - 2:10

score 321 · Answer 13 · 2020-07-24 08:06:42

321

Views

$\Bbb{R}^n$ and $\Bbb{R}$ are isomorphic as vector spaces over $\Bbb{Q}$.

Published on 24 Jul 2020 - 8:06

score 193 · Answer 14 · 2020-07-26 04:50:29

193

Views

Isomorphism Definition - Error in Hoffman Kunze?

Published on 26 Jul 2020 - 4:50

score 86 · Answer 15 · 2020-07-29 02:47:42

86

Views

Prove that $\mathrm{Ker}(T - \lambda I_V)^n = {0}$

Published on 29 Jul 2020 - 2:47

List Question

Isomorphism by restricting surjective linear mapping between finite dimensional spaces, and quotient space by null space

$L_p(\mu,X)$ is isometrically isomorphic to $\ell_p(X)$

Show that $\Bbb{F}^{m×n}$ is isomorphic to $\Bbb{F}^{mn}$.

Let $V$ and $W$ be finite dimensional vector spaces over the field $F$. Prove that $V$ is isomorphic to $W$ iff $dimV=dimW$.

About the existence of an isomorphism of algebras between the algebras of $\mathcal{C}^0$ and $\mathcal{C}^1$ functions from $[0, 1]$ to $\mathbb{R}$

Do theorems concerning isomorphisms that apply to Vector spaces also apply to subspaces?

If $u$ is an isomorphism of $E$ into $F$, prove that to every $n$ there is $m$ such that $u^{-1}(F_n) \subset E_m$

Isomorphism between $\bigwedge^2\mathbb R^3$ and the dual of $\mathfrak{so}(3)$

Do properties in linear algebra proved by using matrix transformations hold true irrespective of the choice of the bases for the vector spaces?

Question on showing invertibility of function $\Phi: \mathcal{L}(V,W) \to M_{m \times n}(F)$ in regards to establishing an isomorphism.

Homomorphic Image of ideal in Lie algebras

Proving a linear map is surjective

$\Bbb{R}^n$ and $\Bbb{R}$ are isomorphic as vector spaces over $\Bbb{Q}$.

Isomorphism Definition - Error in Hoffman Kunze?

Prove that $\mathrm{Ker}(T - \lambda I_V)^n = {0}$

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