Question

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

score 55 · Answer 1 · 2026-04-14 14:26:40

55

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

Published on 14 Apr 2026 - 14:26

score 290 · Answer 2 · 2026-04-15 03:12:50

290

Views

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

Published on 15 Apr 2026 - 3:12

score 108 · Answer 3 · 2026-04-12 20:12:33

108

Views

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

Published on 12 Apr 2026 - 20:12

score 203 · Answer 4 · 2026-04-15 09:08:55

203

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 15 Apr 2026 - 9:08

score 34 · Answer 5 · 2026-04-16 02:12:50

34

Views

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

Published on 16 Apr 2026 - 2:12

score 293 · Answer 6 · 2026-04-11 10:01:24

293

Views

Ways to check positive definiteness of bilinear form

Published on 11 Apr 2026 - 10:01

score 173 · Answer 7 · 2026-04-13 06:50:18

173

Views

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

Published on 13 Apr 2026 - 6:50

score 51 · Answer 8 · 2026-04-16 12:12:36

51

Views

To show orthogonal basis exist consisting common eigenvectors

Published on 16 Apr 2026 - 12:12

score 74 · Answer 9 · 2026-04-11 12:58:12

74

Views

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

Published on 11 Apr 2026 - 12:58

score 246 · Answer 10 · 2026-04-13 19:10:17

246

Views

bilinear form only positive or negative

Published on 13 Apr 2026 - 19:10

score 127 · Answer 11 · 2026-04-15 09:42:45

127

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 15 Apr 2026 - 9:42

score 46 · Answer 12 · 2026-04-14 18:04:01

46

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 14 Apr 2026 - 18:04

score 483 · Answer 13 · 2026-04-12 22:17:44

483

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 12 Apr 2026 - 22:17

score 118 · Answer 14 · 2026-04-13 05:52:15

118

Views

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

Published on 13 Apr 2026 - 5:52

score 83 · Answer 15 · 2026-04-13 16:47:40

83

Views

Process of finding orthonormal basis of given bilinear form

Published on 13 Apr 2026 - 16:47

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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