List questions from vector-space-isomorphism

Published on 31 Jan 2022 - 1:08

75

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Using Third Isomorphism Theorem on Vector Spaces

Published on 31 Jan 2022 - 12:33

60

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How is $T$ an isomorphism?

Published on 02 Feb 2022 - 2:56

198

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Motivation for Proposition 3.14 from Lee's Introduction to smooth manifolds

Published on 08 Feb 2022 - 10:13

54

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Reflexive Banach space.

Published on 23 Feb 2026 - 11:44

48

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Differential of the map $(f_1, f_2) : M \to N_1 \times N_2$.

Published on 26 Mar 2026 - 2:48

38

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Isomorphism and transformation matrix in Linear maps

Published on 13 Feb 2022 - 14:58

79

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Difficulty understanding the link between the span of a sequence being an isomorph of $\ell_1$ and that sequence being a basis of the closed span

Published on 26 Mar 2026 - 8:00

307

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Isomorphism between two vector spaces

Published on 23 Feb 2022 - 13:44

239

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Say whether $V = \mathcal{P}_{3}(\mathbb{R})$ is isomorphic to $W = M_{2\times 2}(\mathbb{R})$ and if it is give an isomorphism.

Published on 24 Feb 2022 - 17:15

78

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Is $T\in \mathcal{L}(V)$ always injective?

Published on 24 Feb 2022 - 17:17

57

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Representations of $\mathfrak{u}(1)$ on $\mathbb{C}$ and $\bar{\mathbb{C}}$ with winding number $k\neq0$ are not isomorphic.

Published on 06 Mar 2022 - 23:17

341

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Confusion Regarding Isomorphisms of Representations

Published on 07 Mar 2022 - 20:53

205

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Isomorphism between $\mathbb{C}^{n}$ and the Complexification of $\mathbb{R}^{n}$

Published on 09 Mar 2022 - 22:43

43

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Isomorphisms between $C([a,b])$ and some subspaces

Published on 13 Mar 2022 - 11:10

List Question

Hilbert space via isomorphism

Using Third Isomorphism Theorem on Vector Spaces

How is $T$ an isomorphism?

Motivation for Proposition 3.14 from Lee's Introduction to smooth manifolds

Reflexive Banach space.

Differential of the map $(f_1, f_2) : M \to N_1 \times N_2$.

Isomorphism and transformation matrix in Linear maps

Difficulty understanding the link between the span of a sequence being an isomorph of $\ell_1$ and that sequence being a basis of the closed span

Isomorphism between two vector spaces

Say whether $V = \mathcal{P}_{3}(\mathbb{R})$ is isomorphic to $W = M_{2\times 2}(\mathbb{R})$ and if it is give an isomorphism.

Is $T\in \mathcal{L}(V)$ always injective?

Representations of $\mathfrak{u}(1)$ on $\mathbb{C}$ and $\bar{\mathbb{C}}$ with winding number $k\neq0$ are not isomorphic.

Confusion Regarding Isomorphisms of Representations

Isomorphism between $\mathbb{C}^{n}$ and the Complexification of $\mathbb{R}^{n}$

Isomorphisms between $C([a,b])$ and some subspaces

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