Question

Proving that the orthogonal group corresponding to a non-degenerate symmetric bilinear form over $\mathbb{C}$ is conjugate to $O(n,\mathbb{C})$?

score 112 · Answer 1 · 2022-06-21 19:43:16

112

Views

Proving that the orthogonal group corresponding to a non-degenerate symmetric bilinear form over $\mathbb{C}$ is conjugate to $O(n,\mathbb{C})$?

Published on 21 Jun 2022 - 19:43

score 410 · Answer 2 · 2022-06-21 20:06:47

410

Views

Is a bilinear form a tensor or a scalar "output'' of that tensor?

Published on 21 Jun 2022 - 20:06

score 62 · Answer 3 · 2026-03-30 04:24:03

62

Views

Galois group and trace form

Published on 30 Mar 2026 - 4:24

score 26 · Answer 4 · 2022-06-25 21:27:04

Is a hermitian form $F$ on $V=\mathbb{C}^n$, which is invariant under a group $H$ acting irreducible on $\mathbb{C}^n$, non-degenerate?

score 42 · Answer 5 · 2022-06-26 18:04:25

42

Views

Question regarding the entries of a matrix $X$ satisfying $g^t X \overline{g}=X$, where $g$ is in companion form.

Published on 26 Jun 2022 - 18:04

score 71 · Answer 6 · 2022-06-26 18:48:05

71

Views

Given a matrix how to determine wether it correspond to a given bilinear form or not?

Published on 26 Jun 2022 - 18:48

score 25 · Answer 7 · 2022-06-27 17:26:40

25

Views

Are real subgroups of $O_F(\mathbb{C})$ contained in $O_F(\mathbb{R})$?

Published on 27 Jun 2022 - 17:26

score 220 · Answer 8 · 2022-06-28 10:59:27

220

Views

Showing that a bilinear form is positive-definite

Published on 28 Jun 2022 - 10:59

score 60 · Answer 9 · 2026-03-29 04:44:00

60

Views

Why is there a $\frac{1}{2}$ term in the equation $B(\delta u, u) = \frac{1}{2} \delta[B(u,u)]$ ? B is bilinear and symmetric

Published on 29 Mar 2026 - 4:44

score 40 · Answer 10 · 2026-03-28 01:07:27

40

Views

How to prove that the is A and a product of reflections R is an element of SO(V)?

Published on 28 Mar 2026 - 1:07

score 42 · Answer 11 · 2022-07-05 08:27:33

42

Views

Does $\lim_{y\to x}\frac{|B(y_1-x_1,y_2-x_2)|}{\|(y_1-x_1,y_2-x_2)\|}$ always approach 0 for a bilinear map $B$?

Published on 05 Jul 2022 - 8:27

score 55 · Answer 12 · 2022-07-11 15:47:41

55

Views

Show that $\beta(f,g)=\int_0^1 f(x)g'(x)dx$ is nondegenerate.

Published on 11 Jul 2022 - 15:47

score 80 · Answer 13 · 2026-03-28 01:12:50

80

Views

There is at most one orthogonal reflection for a given reflection line

Published on 28 Mar 2026 - 1:12

score 162 · Answer 14 · 2026-03-27 07:49:29

162

Views

Why is $B_\pi$ an invariant bilinear form on $\mathfrak{g}$?

Published on 27 Mar 2026 - 7:49

score 89 · Answer 15 · 2022-08-01 08:13:39

89

Views

How to show that $x^t A x $ is divisible by $2$ where $A$ is an $n \times n$ symmetric matrix with all its diagonal entries are zero?

Published on 01 Aug 2022 - 8:13

List Question

Proving that the orthogonal group corresponding to a non-degenerate symmetric bilinear form over $\mathbb{C}$ is conjugate to $O(n,\mathbb{C})$?

Is a bilinear form a tensor or a scalar "output'' of that tensor?

Galois group and trace form

Is a hermitian form $F$ on $V=\mathbb{C}^n$, which is invariant under a group $H$ acting irreducible on $\mathbb{C}^n$, non-degenerate?

Question regarding the entries of a matrix $X$ satisfying $g^t X \overline{g}=X$, where $g$ is in companion form.

Given a matrix how to determine wether it correspond to a given bilinear form or not?

Are real subgroups of $O_F(\mathbb{C})$ contained in $O_F(\mathbb{R})$?

Showing that a bilinear form is positive-definite

Why is there a $\frac{1}{2}$ term in the equation $B(\delta u, u) = \frac{1}{2} \delta[B(u,u)]$ ? B is bilinear and symmetric

How to prove that the is A and a product of reflections R is an element of SO(V)?

Does $\lim_{y\to x}\frac{|B(y_1-x_1,y_2-x_2)|}{\|(y_1-x_1,y_2-x_2)\|}$ always approach 0 for a bilinear map $B$?

Show that $\beta(f,g)=\int_0^1 f(x)g'(x)dx$ is nondegenerate.

There is at most one orthogonal reflection for a given reflection line

Why is $B_\pi$ an invariant bilinear form on $\mathfrak{g}$?

How to show that $x^t A x $ is divisible by $2$ where $A$ is an $n \times n$ symmetric matrix with all its diagonal entries are zero?

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