Question

score 37 · Answer 1 · 2026-03-25 22:26:03

37

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Rewriting $\vec x_1\cdot \vec x_2 |\vec x_3|+\vec x_2\cdot \vec x_3 |\vec x_1|+\vec x_3\cdot \vec x_1 |\vec x_2|$?

Published on 25 Mar 2026 - 22:26

score 467 · Answer 2 · 2026-03-25 11:09:58

467

Views

How does index notation work in Hermitian spaces?

Published on 25 Mar 2026 - 11:09

score 1.1k · Answer 3 · 2026-03-30 18:18:42

1.1k

Views

When does an inner product induce a norm?

Published on 30 Mar 2026 - 18:18

score 1.4k · Answer 4 · 2018-10-15 13:20:18

1.4k

Views

Geometric interpretation of $\|a+b\|^2 +\|a-b\|^2 = 2 \|a\|^2 +2\|b\|^2$

Published on 15 Oct 2018 - 13:20

score 201 · Answer 5 · 2026-03-25 04:42:31

201

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 25 Mar 2026 - 4:42

score 59 · Answer 6 · 2026-03-27 09:15:21

59

Views

$\lVert tx +y\rVert\ge 0$, for all $t\in\mathbb R$, implies that $\,|\langle x,y\rangle|\le \lVert x\rVert \lVert y \rVert$

Published on 27 Mar 2026 - 9:15

score 35 · Answer 7 · 2018-10-19 14:30:34

35

Views

Impossible to conclude about limit even if we have a strong inequality

Published on 19 Oct 2018 - 14:30

score 268 · Answer 8 · 2026-03-27 22:03:24

268

Views

What does Weierstrass Approximation Theorem tell us?

Published on 27 Mar 2026 - 22:03

score 74 · Answer 9 · 2026-03-26 06:06:49

74

Views

$U$ invertible and $U^{\ast}U=1$ then $UU^{\ast}=1$ (Barry Simon)

Published on 26 Mar 2026 - 6:06

score 314 · Answer 10 · 2026-03-27 09:03:36

314

Views

A symmetry of the Hodge star operator

Published on 27 Mar 2026 - 9:03

score 33 · Answer 11 · 2018-10-22 23:48:21

33

Views

Confusion about inner product spaces

Published on 22 Oct 2018 - 23:48

score 1.5k · Answer 12 · 2026-03-25 09:25:29

1.5k

Views

$T^{\ast}T$ unitary then $T$ isometry

Published on 25 Mar 2026 - 9:25

score 138 · Answer 13 · 2018-10-23 12:37:17

138

Views

Showing that a set is closed in an inner product space over a field.

Published on 23 Oct 2018 - 12:37

score 591 · Answer 14 · 2018-10-24 21:04:22

591

Views

Orthogonal Complement of Orthogonal Complement equals to closure of span

Published on 24 Oct 2018 - 21:04

score 1.1k · Answer 15 · 2026-03-26 17:14:25

1.1k

Views

Orthogonality of a matrix where inner product is not the dot product

Published on 26 Mar 2026 - 17:14

List Question

Rewriting $\vec x_1\cdot \vec x_2 |\vec x_3|+\vec x_2\cdot \vec x_3 |\vec x_1|+\vec x_3\cdot \vec x_1 |\vec x_2|$?

How does index notation work in Hermitian spaces?

When does an inner product induce a norm?

Geometric interpretation of $\|a+b\|^2 +\|a-b\|^2 = 2 \|a\|^2 +2\|b\|^2$

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.

$\lVert tx +y\rVert\ge 0$, for all $t\in\mathbb R$, implies that $\,|\langle x,y\rangle|\le \lVert x\rVert \lVert y \rVert$

Impossible to conclude about limit even if we have a strong inequality

What does Weierstrass Approximation Theorem tell us?

$U$ invertible and $U^{\ast}U=1$ then $UU^{\ast}=1$ (Barry Simon)

A symmetry of the Hodge star operator

Confusion about inner product spaces

$T^{\ast}T$ unitary then $T$ isometry

Showing that a set is closed in an inner product space over a field.

Orthogonal Complement of Orthogonal Complement equals to closure of span

Orthogonality of a matrix where inner product is not the dot product

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