List questions from vector-space-isomorphism

205

Views

Which rings containing the complex field are, as vector spaces over that field, isomorphic to $\mathbb{C}^2$?

Published on 08 Nov 2014 - 7:41

280

Views

Can we show it without involving that $V=V^{**}$ are canonically isomorphic?

Published on 22 Nov 2014 - 10:50

200

Views

Isomorphism from a subset of $\mathbb{R}^n$ to the space $\mathbb{R}^{n-1}$

Published on 07 Dec 2014 - 12:26

428

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Is it true that $ U \oplus W_1 = U \oplus W_2 \implies W_1 = W_2 $?

Published on 12 Dec 2014 - 5:28

662

Views

Prove there exist an isomorphism

Published on 17 Dec 2014 - 21:46

80

Views

Some Linear Algebra

Published on 25 Mar 2026 - 4:24

29

Views

Peter Lax Isomorphism Excercise

Published on 15 Oct 2019 - 18:10

442

Views

How is the quotient space H/K is isomorphic to the orthogonal complement of K?

Published on 25 Mar 2026 - 11:03

369

Views

$T$ is onto linear transformation from $V$ to $U$,then $V/N(T)$ is isomorphic with $U$.

Published on 22 Oct 2019 - 14:02

121

Views

Isomorphism between a quotient space and a subspace

Published on 25 Mar 2026 - 7:40

764

Views

Show there is an isomorphism between the vector fields and the derivations.

Published on 27 Oct 2019 - 20:10

445

Views

Is the sum of two isomorphic linear transformations also an isomorphism?

Published on 03 Nov 2019 - 22:09

91

Views

Proving $T(v_1),...T(v_n)$ is a basis for the vector space $W$

Published on 04 Nov 2019 - 16:46

664

Views

Finding that two vector spaces are not isomorphic

Published on 05 Nov 2019 - 1:36

279

Views

Isomorphism of a Polynomial Linear Transformation

Published on 06 Nov 2019 - 2:35

List Question

Which rings containing the complex field are, as vector spaces over that field, isomorphic to $\mathbb{C}^2$?

Can we show it without involving that $V=V^{**}$ are canonically isomorphic?

Isomorphism from a subset of $\mathbb{R}^n$ to the space $\mathbb{R}^{n-1}$

Is it true that $ U \oplus W_1 = U \oplus W_2 \implies W_1 = W_2 $?

Prove there exist an isomorphism

Some Linear Algebra

Peter Lax Isomorphism Excercise

How is the quotient space H/K is isomorphic to the orthogonal complement of K?

$T$ is onto linear transformation from $V$ to $U$,then $V/N(T)$ is isomorphic with $U$.

Isomorphism between a quotient space and a subspace

Show there is an isomorphism between the vector fields and the derivations.

Is the sum of two isomorphic linear transformations also an isomorphism?

Proving $T(v_1),...T(v_n)$ is a basis for the vector space $W$

Finding that two vector spaces are not isomorphic

Isomorphism of a Polynomial Linear Transformation

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