Question

if $\operatorname{Ker}(\phi)$ can be generated with a basis of $E$ then $\phi = 0$

score 52 · Answer 1 · 2018-10-03 08:35:42

52

Views

if $\operatorname{Ker}(\phi)$ can be generated with a basis of $E$ then $\phi = 0$

Published on 03 Oct 2018 - 8:35

score 288 · Answer 2 · 2018-10-04 01:22:09

288

Views

Proof verification : T-invariant subspace has T-invariant complement

Published on 04 Oct 2018 - 1:22

score 105 · Answer 3 · 2018-10-08 01:06:34

105

Views

What does "definite" mean for a bilinear form over a finite field?

Published on 08 Oct 2018 - 1:06

score 200 · Answer 4 · 2018-10-17 15:25:16

200

Views

If $\langle T v,v\rangle=\langle v,v\rangle$ for all $v\in V$ satisfying $\langle v,v\rangle=1$, then $T$ is the identity.

Published on 17 Oct 2018 - 15:25

score 31 · Answer 5 · 2018-10-18 21:23:38

31

Views

Show that $(\Omega (\phi)(v_{1}))(v_{2})=\phi(v_{1},v_{2})$ is well defined and is an isomorphism.

Published on 18 Oct 2018 - 21:23

score 290 · Answer 6 · 2018-11-05 13:31:57

290

Views

Ways to check positive definiteness of bilinear form

Published on 05 Nov 2018 - 13:31

score 170 · Answer 7 · 2018-11-05 17:45:18

170

Views

Hermitian form can be written as sum of symmetric and alternating form

Published on 05 Nov 2018 - 17:45

score 48 · Answer 8 · 2018-11-05 18:11:58

48

Views

To show orthogonal basis exist consisting common eigenvectors

Published on 05 Nov 2018 - 18:11

score 71 · Answer 9 · 2018-11-09 19:13:02

71

Views

Bilinear form can be written as sum of hermitian and symmetric C bilinear form

Published on 09 Nov 2018 - 19:13

score 243 · Answer 10 · 2018-11-12 22:54:11

243

Views

bilinear form only positive or negative

Published on 12 Nov 2018 - 22:54

score 124 · Answer 11 · 2018-11-16 15:57:15

124

Views

Let ${^ts}:E\to F$ be the transpose of $s:F\to E$. Show that $\text{Im}(s)\cap \ker (\,^ts)=\{0_E\}$.

Published on 16 Nov 2018 - 15:57

score 43 · Answer 12 · 2018-11-17 17:12:55

43

Views

bilinear transformation $\phi U\times V\to W$ such that $Im(\phi)=\{\phi(u,v): u\in U, v\in V\}$ is not a subspace of $W$

Published on 17 Nov 2018 - 17:12

score 480 · Answer 13 · 2018-11-25 06:09:38

480

Views

If real Matrix A is symmetric and positive definite then $X^TAY $ represent dot product with respect to basis of $\mathbb R^n$

Published on 25 Nov 2018 - 6:09

score 115 · Answer 14 · 2018-11-25 14:59:07

115

Views

How to show that every symmetric nonsingular complex matrix can be written as $A=P^ T P$ form

Published on 25 Nov 2018 - 14:59

score 80 · Answer 15 · 2018-11-25 15:07:11

80

Views

Process of finding orthonormal basis of given bilinear form

Published on 25 Nov 2018 - 15:07

List Question

if $\operatorname{Ker}(\phi)$ can be generated with a basis of $E$ then $\phi = 0$

Proof verification : T-invariant subspace has T-invariant complement

What does "definite" mean for a bilinear form over a finite field?

If $\langle T v,v\rangle=\langle v,v\rangle$ for all $v\in V$ satisfying $\langle v,v\rangle=1$, then $T$ is the identity.

Show that $(\Omega (\phi)(v_{1}))(v_{2})=\phi(v_{1},v_{2})$ is well defined and is an isomorphism.

Ways to check positive definiteness of bilinear form

Hermitian form can be written as sum of symmetric and alternating form

To show orthogonal basis exist consisting common eigenvectors

Bilinear form can be written as sum of hermitian and symmetric C bilinear form

bilinear form only positive or negative

Let ${^ts}:E\to F$ be the transpose of $s:F\to E$. Show that $\text{Im}(s)\cap \ker (\,^ts)=\{0_E\}$.

bilinear transformation $\phi U\times V\to W$ such that $Im(\phi)=\{\phi(u,v): u\in U, v\in V\}$ is not a subspace of $W$

If real Matrix A is symmetric and positive definite then $X^TAY $ represent dot product with respect to basis of $\mathbb R^n$

How to show that every symmetric nonsingular complex matrix can be written as $A=P^ T P$ form

Process of finding orthonormal basis of given bilinear form

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