Question

Showing that the isomorphism of the general linear group of a vector space with the group of invertible matrices is smooth

score 100 · Answer 1 · 2024-01-05 18:49:12

100

Views

Showing that the isomorphism of the general linear group of a vector space with the group of invertible matrices is smooth

Published on 05 Jan 2024 - 18:49

score 33 · Answer 2 · 2024-01-12 02:27:59

33

Views

Some property of GL(2,R) and GL(2,Z)

Published on 12 Jan 2024 - 2:27

score 720 · Answer 3 · 2024-01-27 02:49:37

720

Views

What are the continuous outer automorphisms of the general linear group?

Published on 27 Jan 2024 - 2:49

score 84 · Answer 4 · 2024-01-29 20:57:27

84

Views

Show that as groups, $\mathrm{GL}(V)\cong\mathrm{GL}_n(\mathbb{F})$, with the isomorphism given by $\theta \mapsto A_\theta$

Published on 29 Jan 2024 - 20:57

score 26 · Answer 5 · 2024-01-31 15:21:49

26

Views

Splitting a matrix of two variables into matrices of one variable

Published on 31 Jan 2024 - 15:21

score 85 · Answer 6 · 2024-02-14 14:00:05

85

Views

When is the quotient of $\operatorname{GL}_n(\mathbb{R})$ by a discrete subgroup compact?

Published on 14 Feb 2024 - 14:00

score 34 · Answer 7 · 2024-02-16 04:18:22

34

Views

Parameterization of Irreducible Representations of $\text{GL}_m(\mathbb{C})$

Published on 16 Feb 2024 - 4:18

score 15 · Answer 8 · 2026-03-04 21:09:38

15

Views

Decomposing (unimodular) matrix over integers into product of matrices mod d

Published on 04 Mar 2026 - 21:09

score 85 · Answer 9 · 2026-02-23 03:59:17

85

Views

Does there exist an element of order $4$ in $GL_2(\mathbb{Z})/GL_2(\mathbb{Z})'$?

Published on 23 Feb 2026 - 3:59

score 28 · Answer 10 · 2026-03-25 03:20:22

28

Views

Linear algebraic interpretation of exceptional normal subgroup of $\mathrm{GL}_2(K)$

Published on 25 Mar 2026 - 3:20

score 741 · Answer 11 · 2026-03-19 16:53:32

741

Views

Is there a surjective group homomorphism $\operatorname{GL}_{n}(k) \to \operatorname{GL}_{m}(k)$ where $n > m$?

Published on 19 Mar 2026 - 16:53

score 5.3k · Answer 12 · 2017-04-10 02:57:13

5.3k

Views

Prove that $\mathbb{C}^*$ is isomorphic to a subgroup of $GL_2(\mathbb{R})$

Published on 10 Apr 2017 - 2:57

score 871 · Answer 13 · 2017-08-13 15:01:32

871

Views

Irreducible finite dimensional complex representation of $GL_2(\Bbb C)$

Published on 13 Aug 2017 - 15:01

score 109 · Answer 14 · 2020-08-10 14:31:55

109

Views

Show that the group operation of conjugation is compatible with the bilinear form $\langle A,B\rangle=1/2 \textrm{ trace }AB$

Published on 10 Aug 2020 - 14:31

score 241 · Answer 15 · 2020-09-13 09:43:43

241

Views

Show that the $GL(n,\mathbb R)/P_k$ is isomorphic to the $GL(n,\mathbb R)$-set grassmannian.

Published on 13 Sep 2020 - 9:43

List Question

Showing that the isomorphism of the general linear group of a vector space with the group of invertible matrices is smooth

Some property of GL(2,R) and GL(2,Z)

What are the continuous outer automorphisms of the general linear group?

Show that as groups, $\mathrm{GL}(V)\cong\mathrm{GL}_n(\mathbb{F})$, with the isomorphism given by $\theta \mapsto A_\theta$

Splitting a matrix of two variables into matrices of one variable

When is the quotient of $\operatorname{GL}_n(\mathbb{R})$ by a discrete subgroup compact?

Parameterization of Irreducible Representations of $\text{GL}_m(\mathbb{C})$

Decomposing (unimodular) matrix over integers into product of matrices mod d

Does there exist an element of order $4$ in $GL_2(\mathbb{Z})/GL_2(\mathbb{Z})'$?

Linear algebraic interpretation of exceptional normal subgroup of $\mathrm{GL}_2(K)$

Is there a surjective group homomorphism $\operatorname{GL}_{n}(k) \to \operatorname{GL}_{m}(k)$ where $n > m$?

Prove that $\mathbb{C}^*$ is isomorphic to a subgroup of $GL_2(\mathbb{R})$

Irreducible finite dimensional complex representation of $GL_2(\Bbb C)$

Show that the group operation of conjugation is compatible with the bilinear form $\langle A,B\rangle=1/2 \textrm{ trace }AB$

Show that the $GL(n,\mathbb R)/P_k$ is isomorphic to the $GL(n,\mathbb R)$-set grassmannian.

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