Question

$\mathcal{H}$ is Hilbert space. A finite subtset of vectors $S = \{x_1, x_2, ..., x_n\}$ must have at least two identical vectors if:

score 49 · Answer 1 · 2026-04-14 10:17:19

49

Views

$\mathcal{H}$ is Hilbert space. A finite subtset of vectors $S = \{x_1, x_2, ..., x_n\}$ must have at least two identical vectors if:

Published on 14 Apr 2026 - 10:17

score 29 · Answer 2 · 2026-04-11 20:47:34

29

Views

Closeness of Complex Function

Published on 11 Apr 2026 - 20:47

score 70 · Answer 3 · 2026-04-12 15:02:29

70

Views

How to proof whether these vectors are orthogonal?

Published on 12 Apr 2026 - 15:02

score 70 · Answer 4 · 2026-04-24 09:38:45

70

Views

Is it possible to square vector like this?

Published on 24 Apr 2026 - 9:38

score 140 · Answer 5 · 2026-04-13 11:11:44

140

Views

Lower bound for inner product between "close" vectors

Published on 13 Apr 2026 - 11:11

score 51 · Answer 6 · 2026-04-13 10:32:57

51

Views

Bounded orthogonal sequence in unitary space.

Published on 13 Apr 2026 - 10:32

score 67 · Answer 7 · 2026-04-16 12:28:05

67

Views

Continuity and differentiability of $f\colon M_n(\Bbb R) \to \Bbb R$ defined by $f(A) = \langle A^2x,x\rangle$, where $x \in \Bbb R^n$ is fixed

Published on 16 Apr 2026 - 12:28

score 166 · Answer 8 · 2026-04-15 02:07:48

166

Views

Schwarz inequality and general proof

Published on 15 Apr 2026 - 2:07

score 203 · Answer 9 · 2026-04-14 11:39:38

203

Views

Distances between points on a sphere determine them up to isometry

Published on 14 Apr 2026 - 11:39

score 40 · Answer 10 · 2026-04-16 02:37:19

40

Views

The distance to a linearly independent vectors on the sphere determines a point uniquely

Published on 16 Apr 2026 - 2:37

score 96 · Answer 11 · 2026-04-13 21:48:38

96

Views

Let $L_0 = (-i)^m \frac{d^m u}{dx^m}$. How can I prove, that $L_0$ is a non-negative operator?

Published on 13 Apr 2026 - 21:48

score 45 · Answer 12 · 2026-04-13 20:07:45

45

Views

Prove that $L_0 = (-i)^m \frac{d^m u}{dx^m}$ is a positive operator

Published on 13 Apr 2026 - 20:07

score 42 · Answer 13 · 2026-04-13 10:50:45

42

Views

Geometry - I am getting two different results when using two different scalar product properties

Published on 13 Apr 2026 - 10:50

score 222 · Answer 14 · 2026-04-14 05:17:43

222

Views

Are Isomorphic Hilbert spaces always isometric?

Published on 14 Apr 2026 - 5:17

score 84 · Answer 15 · 2026-04-14 07:04:00

84

Views

Why matrix dot product (in linear algebra) is equal to vector dot product (in geometry)? A link between linear transformation and vector projection?

Published on 14 Apr 2026 - 7:04

List Question

$\mathcal{H}$ is Hilbert space. A finite subtset of vectors $S = \{x_1, x_2, ..., x_n\}$ must have at least two identical vectors if:

Closeness of Complex Function

How to proof whether these vectors are orthogonal?

Is it possible to square vector like this?

Lower bound for inner product between "close" vectors

Bounded orthogonal sequence in unitary space.

Continuity and differentiability of $f\colon M_n(\Bbb R) \to \Bbb R$ defined by $f(A) = \langle A^2x,x\rangle$, where $x \in \Bbb R^n$ is fixed

Schwarz inequality and general proof

Distances between points on a sphere determine them up to isometry

The distance to a linearly independent vectors on the sphere determines a point uniquely

Let $L_0 = (-i)^m \frac{d^m u}{dx^m}$. How can I prove, that $L_0$ is a non-negative operator?

Prove that $L_0 = (-i)^m \frac{d^m u}{dx^m}$ is a positive operator

Geometry - I am getting two different results when using two different scalar product properties

Are Isomorphic Hilbert spaces always isometric?

Why matrix dot product (in linear algebra) is equal to vector dot product (in geometry)? A link between linear transformation and vector projection?

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