Question

Cauchy-Schwarz inequality with non-standard dot product

score 326 · Answer 1 · 2026-04-12 01:04:00

326

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Cauchy-Schwarz inequality with non-standard dot product

Published on 12 Apr 2026 - 1:04

score 75 · Answer 2 · 2026-04-15 16:41:47

75

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Isotropic subspace of $x_1^2-x_2^2+x_3^2$

Published on 15 Apr 2026 - 16:41

score 156 · Answer 3 · 2026-04-13 20:32:42

156

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Show that a convergent orthogonal sequence in a Hilbert space has limit zero

Published on 13 Apr 2026 - 20:32

score 46 · Answer 4 · 2026-04-16 09:34:21

46

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$\min_{x\in\mathbb{R}^n}(\langle z,x-y\rangle+\lVert x-y\rVert^2)=\min_{r\ge0}(-r\lVert z\rVert+r^2)$

Published on 16 Apr 2026 - 9:34

score 35 · Answer 5 · 2026-04-15 07:29:10

35

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Why is the variance of 2 dot products sampled from a uniform distribution $1/n$?

Published on 15 Apr 2026 - 7:29

score 74 · Answer 6 · 2026-04-14 13:25:37

74

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If $A$ is a norm-preserving linear map (+ other conditions), then it is an isometry

Published on 14 Apr 2026 - 13:25

score 218 · Answer 7 · 2026-05-06 17:22:15

218

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given the dot and cross products of vectors b and v, solve for v

Published on 06 May 2026 - 17:22

score 156 · Answer 8 · 2026-04-16 11:50:39

156

Views

proof: when the dot product of a number of vectors and a specific vector is constant, those vectors are on the same line orthogonal to the vector.

Published on 16 Apr 2026 - 11:50

score 46 · Answer 9 · 2026-04-12 13:48:42

46

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Connection between inner products over prime fields and finite non-prime fields

Published on 12 Apr 2026 - 13:48

score 121 · Answer 10 · 2026-04-15 14:18:05

121

Views

Gram-Schmidt in a linearly independent set.

Published on 15 Apr 2026 - 14:18

score 56 · Answer 11 · 2026-04-15 20:25:35

56

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Intuition for the choice of vector when showing that $(\forall\psi\in H:\left<\psi\mid T\psi\right>=0)\implies T=0$ for a bounded operator $T$

Published on 15 Apr 2026 - 20:25

score 57 · Answer 12 · 2026-04-16 16:04:24

57

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Prove that $\frac{1}{|| x|| \cdot|| y||} | \langle x, y \rangle | = | \langle \frac{ x}{|| x||}, \frac{ y}{|| y||} \rangle |$

Published on 16 Apr 2026 - 16:04

score 63 · Answer 13 · 2026-04-13 03:05:46

63

Views

Applications of angles in infinite-dimensional inner product spaces

Published on 13 Apr 2026 - 3:05

List Question

Cauchy-Schwarz inequality with non-standard dot product

Isotropic subspace of $x_1^2-x_2^2+x_3^2$

Show that a convergent orthogonal sequence in a Hilbert space has limit zero

$\min_{x\in\mathbb{R}^n}(\langle z,x-y\rangle+\lVert x-y\rVert^2)=\min_{r\ge0}(-r\lVert z\rVert+r^2)$

Why is the variance of 2 dot products sampled from a uniform distribution $1/n$?

If $A$ is a norm-preserving linear map (+ other conditions), then it is an isometry

given the dot and cross products of vectors b and v, solve for v

proof: when the dot product of a number of vectors and a specific vector is constant, those vectors are on the same line orthogonal to the vector.

Connection between inner products over prime fields and finite non-prime fields

Gram-Schmidt in a linearly independent set.

Intuition for the choice of vector when showing that $(\forall\psi\in H:\left<\psi\mid T\psi\right>=0)\implies T=0$ for a bounded operator $T$

Prove that $\frac{1}{|| x|| \cdot|| y||} | \langle x, y \rangle | = | \langle \frac{ x}{|| x||}, \frac{ y}{|| y||} \rangle |$

Applications of angles in infinite-dimensional inner product spaces

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