Question

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

score 101 · Answer 1 · 2026-03-25 12:49:52

101

Views

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

Published on 25 Mar 2026 - 12:49

score 34 · Answer 2 · 2026-03-25 12:54:27

34

Views

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

Published on 25 Mar 2026 - 12:54

score 721 · Answer 3 · 2026-03-25 12:53:07

721

Views

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

Published on 25 Mar 2026 - 12:53

score 85 · Answer 4 · 2026-03-25 12:54:33

85

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 25 Mar 2026 - 12:54

score 27 · Answer 5 · 2026-03-25 12:53:19

27

Views

Splitting a matrix of two variables into matrices of one variable

Published on 25 Mar 2026 - 12:53

score 87 · Answer 6 · 2026-05-10 19:21:11

87

Views

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

Published on 10 May 2026 - 19:21

score 35 · Answer 7 · 2026-03-25 12:53:41

35

Views

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

Published on 25 Mar 2026 - 12:53

score 17 · Answer 8 · 2026-04-16 01:41:53

17

Views

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

Published on 16 Apr 2026 - 1:41

score 86 · Answer 9 · 2026-04-09 08:06:58

86

Views

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

Published on 09 Apr 2026 - 8:06

score 29 · Answer 10 · 2026-05-10 16:56:42

29

Views

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

Published on 10 May 2026 - 16:56

score 746 · Answer 11 · 2026-04-09 20:31:48

746

Views

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

Published on 09 Apr 2026 - 20:31

score 5.3k · Answer 12 · 2026-03-25 14:23:52

5.3k

Views

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

Published on 25 Mar 2026 - 14:23

score 872 · Answer 13 · 2026-03-25 12:53:44

872

Views

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

Published on 25 Mar 2026 - 12:53

score 110 · Answer 14 · 2026-03-25 14:24:38

110

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 25 Mar 2026 - 14:24

score 242 · Answer 15 · 2026-03-25 14:25:52

242

Views

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

Published on 25 Mar 2026 - 14:25

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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