Question

Proof about L(U,V). Is this reasoning correct?

score 59 · Answer 1 · 2022-03-14 15:01:01

59

Views

Proof about L(U,V). Is this reasoning correct?

Published on 14 Mar 2022 - 15:01

score 80 · Answer 2 · 2022-03-22 02:40:22

80

Views

Isomorphism and Identification between Vector Spaces

Published on 22 Mar 2022 - 2:40

score 26 · Answer 3 · 2022-04-25 13:48:33

26

Views

Suppose that $dim(U) = dim (V)<\infty$ and let $T\in Hom(U,V)$. If $AT=\iota_V$ or $TA=\iota_U$, then $A$ is an isomorphism and $A^{-1}=T$.

Published on 25 Apr 2022 - 13:48

score 35 · Answer 4 · 2026-03-27 09:17:40

35

Views

Are field isomorphisms necessarily linear isomorphisms?

Published on 27 Mar 2026 - 9:17

score 57 · Answer 5 · 2026-03-27 14:03:33

57

Views

If ring endomorphisms of finite dimensional vector spaces are isomorphic => Vector spaces and division rings are isomorphic

Published on 27 Mar 2026 - 14:03

score 131 · Answer 6 · 2022-05-19 08:17:36

131

Views

Exercise 3.E.12 on p.99 in "Linear Algebra Done Right 3rd Edition" by Sheldon Axler. Is my solution ok? What is a typical solution to this exercise?

Published on 19 May 2022 - 8:17

score 241 · Answer 7 · 2022-05-23 09:11:55

241

Views

Exercise 3.F.5 in "Linear Algebra Done Right 3rd Edition" by Sheldon Axler.

Published on 23 May 2022 - 9:11

score 89 · Answer 8 · 2022-05-26 00:14:11

89

Views

A canonical isomorphism from $V$ to $W$.

Published on 26 May 2022 - 0:14

score 33 · Answer 9 · 2022-05-27 04:10:59

33

Views

Why is this proof valid when n = 0 (dimension is equal to 0)?

Published on 27 May 2022 - 4:10

score 59 · Answer 10 · 2022-05-27 20:32:29

Let f be a correspondence between vector spaces V& W. Show that the spaces V & W are isomorphic via f if and only if (rest of question inside) ...

score 130 · Answer 11 · 2022-05-30 12:30:39

Need to prove if two vector spaces are isomorphic, then they have the same dimension? ("Linear Algebra Done Right 3rd Edition" by Sheldon Axler)

score 227 · Answer 12 · 2022-05-30 22:03:40

227

Views

Is the set of isomorphisms from a vector space to itself a subspace of the space L(V, V) of homomorphisms from the space to itself?

Published on 30 May 2022 - 22:03

score 269 · Answer 13 · 2022-05-31 12:00:27

269

Views

Show this two Lie algebras are isomorphic

Published on 31 May 2022 - 12:00

score 616 · Answer 14 · 2022-06-07 15:06:14

616

Views

What is the reason that isomorphisms between vector spaces are invertible?

Published on 07 Jun 2022 - 15:06

score 267 · Answer 15 · 2022-06-10 16:37:17

267

Views

How to find the image of an element of the domain?

Published on 10 Jun 2022 - 16:37

List Question

Proof about L(U,V). Is this reasoning correct?

Isomorphism and Identification between Vector Spaces

Suppose that $dim(U) = dim (V)<\infty$ and let $T\in Hom(U,V)$. If $AT=\iota_V$ or $TA=\iota_U$, then $A$ is an isomorphism and $A^{-1}=T$.

Are field isomorphisms necessarily linear isomorphisms?

If ring endomorphisms of finite dimensional vector spaces are isomorphic => Vector spaces and division rings are isomorphic

Exercise 3.E.12 on p.99 in "Linear Algebra Done Right 3rd Edition" by Sheldon Axler. Is my solution ok? What is a typical solution to this exercise?

Exercise 3.F.5 in "Linear Algebra Done Right 3rd Edition" by Sheldon Axler.

A canonical isomorphism from $V$ to $W$.

Why is this proof valid when n = 0 (dimension is equal to 0)?

Let f be a correspondence between vector spaces V& W. Show that the spaces V & W are isomorphic via f if and only if (rest of question inside) ...

Need to prove if two vector spaces are isomorphic, then they have the same dimension? ("Linear Algebra Done Right 3rd Edition" by Sheldon Axler)

Is the set of isomorphisms from a vector space to itself a subspace of the space L(V, V) of homomorphisms from the space to itself?

Show this two Lie algebras are isomorphic

What is the reason that isomorphisms between vector spaces are invertible?

How to find the image of an element of the domain?

Trending Questions

Popular # Hahtags

Popular Questions