List questions from vector-space-isomorphism

Published on 29 Aug 2022 - 10:42

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Isomorphism of associated graded vector spaces implies an isomorphism of vector spaces

Published on 26 Mar 2026 - 19:02

82

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Theorem 3, Section 4.3 of Hoffman’s Linear Algebra

Published on 07 Sep 2022 - 17:57

16

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Is the set of arithmetic progressions isomorphic to $F^2$?

Published on 12 Sep 2022 - 8:00

61

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Show that $L_{l}(X)$ is isomorphic to $L(X/Im(l),Ker(l))$

Published on 25 Sep 2022 - 19:26

166

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Isomorphism between quotient spaces?

Published on 06 Oct 2022 - 10:32

174

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How to prove $\operatorname{rank}(M \circ L) <= rank(M)$ if $L$ and $M$ is inverse mapping of $L$

Published on 10 Oct 2022 - 12:52

70

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...show that if {$v_1,…,v_n$} is the basis of $V$ such that {$T (v_1),…,T(v_n)$} is a basis of $W$, so $T$ is an isomorphism.

Published on 20 Oct 2022 - 13:28

38

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Quotient spaces-vector spaces

Published on 08 Nov 2022 - 19:39

35

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Using the First Isomorphism Theorem to find a linear transformation

Published on 09 Nov 2022 - 3:58

171

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Clifford Algebra is isomorphic to exterior algebra

Published on 14 Nov 2022 - 21:40

188

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Sobolev spaces are isomorphic to $L^2$?

Published on 19 Nov 2022 - 19:44

50

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Does an isometric automorphism of $L_p := L_p (\Omega, \mu, X)$ preserve the support?

Published on 19 Nov 2022 - 23:05

69

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How to show that $C^{\infty} (X) \otimes C^{\infty} (X) \not\simeq C^{\infty} (X \times X)$ as vector spaces.

Published on 20 Nov 2022 - 4:00

152

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Understand proof: Set of bilinear forms is a vector space

Published on 24 Nov 2022 - 22:55

List Question

Exercise 8, Section 3.7 of Hoffman’s Linear Algebra

Isomorphism of associated graded vector spaces implies an isomorphism of vector spaces

Theorem 3, Section 4.3 of Hoffman’s Linear Algebra

Is the set of arithmetic progressions isomorphic to $F^2$?

Show that $L_{l}(X)$ is isomorphic to $L(X/Im(l),Ker(l))$

Isomorphism between quotient spaces?

How to prove $\operatorname{rank}(M \circ L) <= rank(M)$ if $L$ and $M$ is inverse mapping of $L$

...show that if {$v_1,…,v_n$} is the basis of $V$ such that {$T (v_1),…,T(v_n)$} is a basis of $W$, so $T$ is an isomorphism.

Quotient spaces-vector spaces

Using the First Isomorphism Theorem to find a linear transformation

Clifford Algebra is isomorphic to exterior algebra

Sobolev spaces are isomorphic to $L^2$?

Does an isometric automorphism of $L_p := L_p (\Omega, \mu, X)$ preserve the support?

How to show that $C^{\infty} (X) \otimes C^{\infty} (X) \not\simeq C^{\infty} (X \times X)$ as vector spaces.

Understand proof: Set of bilinear forms is a vector space

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