Question

$T$ be a finite rank operator of rank $n$. There exist orthonormal set $\{u_1,\ldots,u_n\}$ such that $Th=\sum_{i=1}^n\langle h,u_i\rangle Tu_i$

score 59 · Answer 1 · 2023-04-01 21:41:17

59

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$T$ be a finite rank operator of rank $n$. There exist orthonormal set $\{u_1,\ldots,u_n\}$ such that $Th=\sum_{i=1}^n\langle h,u_i\rangle Tu_i$

Published on 01 Apr 2023 - 21:41

score 138 · Answer 2 · 2026-03-27 13:27:18

138

Views

Is this property true for subspaces of a Hilbert Space?

Published on 27 Mar 2026 - 13:27

score 94 · Answer 3 · 2026-03-26 06:27:54

94

Views

Who coined the term Orthonormal?

Published on 26 Mar 2026 - 6:27

score 32 · Answer 4 · 2023-04-15 22:29:16

32

Views

Deriving components of a bra vector using orthonormal basis vectors

Published on 15 Apr 2023 - 22:29

score 69 · Answer 5 · 2026-03-27 07:18:42

69

Views

Does the covariant derivative of the unit normal vector field vanish (in this special case)?

Published on 27 Mar 2026 - 7:18

score 61 · Answer 6 · 2023-04-21 20:43:55

61

Views

How do I show $\frac{1}{\sqrt L}e^{\frac{2\pi inx}{L}}$ is an orthonormal set for $L^2[a, b]$ (where $|b-a|=L$)?

Published on 21 Apr 2023 - 20:43

score 40 · Answer 7 · 2023-04-25 20:19:12

40

Views

Infinite series of squares of elements of orthonormal basis of $L^2(a,b)$

Published on 25 Apr 2023 - 20:19

score 66 · Answer 8 · 2023-04-26 00:34:12

66

Views

Prove the squares of a particular coordinates of all vectors of an orthonormal basis sum to 1

Published on 26 Apr 2023 - 0:34

score 781 · Answer 9 · 2023-04-26 16:27:38

781

Views

Example of an inner product space with no orthonormal basis

Published on 26 Apr 2023 - 16:27

score 72 · Answer 10 · 2023-04-29 16:37:05

72

Views

An example of dense subspace of $\ell_2$

Published on 29 Apr 2023 - 16:37

score 108 · Answer 11 · 2023-05-04 19:25:17

108

Views

Proof of Bessel inequality by orthogonal projectors

Published on 04 May 2023 - 19:25

score 242 · Answer 12 · 2023-05-06 15:46:29

242

Views

Using Gram-Schmidt to extend an orthonormal basis for a subspace

Published on 06 May 2023 - 15:46

score 19 · Answer 13 · 2023-05-11 07:29:36

19

Views

Orthonormal matrix with the least column variance

Published on 11 May 2023 - 7:29

score 225 · Answer 14 · 2023-05-14 18:03:50

225

Views

span of maximal orthonormal sets in a Hilbert space

Published on 14 May 2023 - 18:03

score 60 · Answer 15 · 2023-05-18 10:29:27

60

Views

Determination of tangential and binormal vectors

Published on 18 May 2023 - 10:29

List Question

$T$ be a finite rank operator of rank $n$. There exist orthonormal set $\{u_1,\ldots,u_n\}$ such that $Th=\sum_{i=1}^n\langle h,u_i\rangle Tu_i$

Is this property true for subspaces of a Hilbert Space?

Who coined the term Orthonormal?

Deriving components of a bra vector using orthonormal basis vectors

Does the covariant derivative of the unit normal vector field vanish (in this special case)?

How do I show $\frac{1}{\sqrt L}e^{\frac{2\pi inx}{L}}$ is an orthonormal set for $L^2[a, b]$ (where $|b-a|=L$)?

Infinite series of squares of elements of orthonormal basis of $L^2(a,b)$

Prove the squares of a particular coordinates of all vectors of an orthonormal basis sum to 1

Example of an inner product space with no orthonormal basis

An example of dense subspace of $\ell_2$

Proof of Bessel inequality by orthogonal projectors

Using Gram-Schmidt to extend an orthonormal basis for a subspace

Orthonormal matrix with the least column variance

span of maximal orthonormal sets in a Hilbert space

Determination of tangential and binormal vectors

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