List questions from vector-space-isomorphism

Published on 09 Oct 2021 - 14:41

57

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Why is addition not commutative under PM's notion of relation number?

Published on 26 Mar 2026 - 4:34

37

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Existence of linear map.

Published on 13 Oct 2021 - 19:39

103

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Show that the vector space $V$ over Field $R$ with a basis $B$ and vector space $\text{Map}[B,R]$ are isomorphic.

Published on 17 Nov 2021 - 0:33

85

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Understanding solutions given by transposition

Published on 18 Nov 2021 - 20:15

53

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Let $A \subseteq \mathbb R^m$, $B \subseteq \mathbb R^n$, and $f:A \to B$ be a diffeomorphism. Then $m = n$

Published on 20 Nov 2021 - 16:16

190

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Quotient space projection

Published on 24 Nov 2021 - 11:34

120

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Is C(K) a subalgebra in its bidual?

Published on 25 Nov 2021 - 7:34

72

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Regular matrix and linear transformation map

Published on 25 Nov 2021 - 16:47

65

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$T$ is an isomorphism if and only if there are $c,k>0$ such that $c||x|| \leq ||T(x)|| \leq k||x||$.

Published on 14 Dec 2021 - 19:41

69

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No isomorphism between set of finite and infinite sequences

Published on 20 Dec 2021 - 14:06

207

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Show a vector space has no countable basis

Published on 10 Jan 2022 - 17:38

193

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Show $T: \mathcal{P}_n \rightarrow \mathcal{P}_n$ defined by $T(p(x)) = p(x) + p'(x)$ is an isomorphism

Published on 13 Jan 2022 - 5:22

94

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$F'$ and $E'$ are isomorphic isometrically.

Published on 17 Jan 2022 - 13:33

25

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Compute the dimension of the quotient space $\mathfrak m_a/\mathfrak m_a^2$

Published on 25 Mar 2026 - 11:16

List Question

Is a quotient space isomorphic to its orthogonal

Why is addition not commutative under PM's notion of relation number?

Existence of linear map.

Show that the vector space $V$ over Field $R$ with a basis $B$ and vector space $\text{Map}[B,R]$ are isomorphic.

Understanding solutions given by transposition

Let $A \subseteq \mathbb R^m$, $B \subseteq \mathbb R^n$, and $f:A \to B$ be a diffeomorphism. Then $m = n$

Quotient space projection

Is C(K) a subalgebra in its bidual?

Regular matrix and linear transformation map

$T$ is an isomorphism if and only if there are $c,k>0$ such that $c||x|| \leq ||T(x)|| \leq k||x||$.

No isomorphism between set of finite and infinite sequences

Show a vector space has no countable basis

Show $T: \mathcal{P}_n \rightarrow \mathcal{P}_n$ defined by $T(p(x)) = p(x) + p'(x)$ is an isomorphism

$F'$ and $E'$ are isomorphic isometrically.

Compute the dimension of the quotient space $\mathfrak m_a/\mathfrak m_a^2$

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