Question

Orthonormal Basis of a function

score 202 · Answer 1 · 2026-03-26 14:19:12

202

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Orthonormal Basis of a function

Published on 26 Mar 2026 - 14:19

score 25 · Answer 2 · 2015-07-10 21:22:06

25

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Equivalent definitions of an orthonormal function

Published on 10 Jul 2015 - 21:22

score 1.2k · Answer 3 · 2015-07-18 21:17:34

1.2k

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Proving that an orthonormal system close to a basis is also a basis

Published on 18 Jul 2015 - 21:17

score 1.6k · Answer 4 · 2015-07-22 22:28:01

1.6k

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$\{x \mapsto e^{2\pi i k x} \mid k \in \mathbb{N}\}$ is orthonormal basis of $L^2$

Published on 22 Jul 2015 - 22:28

score 5k · Answer 5 · 2015-07-27 11:00:24

5k

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Normalizing a basis

Published on 27 Jul 2015 - 11:00

score 1.2k · Answer 6 · 2015-08-04 00:01:58

1.2k

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Orthonormality of the columns of a matrix

Published on 04 Aug 2015 - 0:01

score 102 · Answer 7 · 2015-08-06 15:41:35

102

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Equality of two matrices

Published on 06 Aug 2015 - 15:41

score 62 · Answer 8 · 2015-08-11 05:24:24

62

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$\lim_{k \to \infty} \langle s_k,e_n \rangle = \langle h,e_n \rangle$

Published on 11 Aug 2015 - 5:24

score 41 · Answer 9 · 2015-08-12 13:38:49

Simple proof that $\min \|\mathbf{f} - \sum_i \lambda_i\hat{\mathbf{g}_i}\|$ is given by $\lambda_i = \langle \mathbf{f}, \hat{\mathbf{g}}_i \rangle$

score 312 · Answer 10 · 2015-08-18 17:03:03

312

Views

Sufficient Condition for $f\in L^{1}(\mathbb{R}^{d})$ to belong to $L^{2}(\mathbb{R}^{d})$ in terms of its Fourier coefficients

Published on 18 Aug 2015 - 17:03

score 13.5k · Answer 11 · 2015-08-20 13:34:41

13.5k

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What exactly is pairwise orthogonal?

Published on 20 Aug 2015 - 13:34

score 944 · Answer 12 · 2015-08-21 08:25:44

944

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Gram–Schmidt algorithm used for obtaining the orthogonal and orthonormal

Published on 21 Aug 2015 - 8:25

score 39 · Answer 13 · 2015-08-27 15:12:31

39

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Show that the continuum of elements $e^{i\lambda t}$ forms a complete orthonormal subset of $B^2$.

Published on 27 Aug 2015 - 15:12

score 609 · Answer 14 · 2015-09-28 14:17:24

609

Views

If $(e_1,\ldots)$ is an orthonormal basis and $x$ is orthogonal to the $(e_i)$, must $x$ be $0$?

Published on 28 Sep 2015 - 14:17

score 99 · Answer 15 · 2015-10-02 05:41:30

99

Views

Hermitian operator's eigenvectors are not orthonormal and not complete

Published on 02 Oct 2015 - 5:41

List Question

Orthonormal Basis of a function

Equivalent definitions of an orthonormal function

Proving that an orthonormal system close to a basis is also a basis

$\{x \mapsto e^{2\pi i k x} \mid k \in \mathbb{N}\}$ is orthonormal basis of $L^2$

Normalizing a basis

Orthonormality of the columns of a matrix

Equality of two matrices

$\lim_{k \to \infty} \langle s_k,e_n \rangle = \langle h,e_n \rangle$

Simple proof that $\min \|\mathbf{f} - \sum_i \lambda_i\hat{\mathbf{g}_i}\|$ is given by $\lambda_i = \langle \mathbf{f}, \hat{\mathbf{g}}_i \rangle$

Sufficient Condition for $f\in L^{1}(\mathbb{R}^{d})$ to belong to $L^{2}(\mathbb{R}^{d})$ in terms of its Fourier coefficients

What exactly is pairwise orthogonal?

Gram–Schmidt algorithm used for obtaining the orthogonal and orthonormal

Show that the continuum of elements $e^{i\lambda t}$ forms a complete orthonormal subset of $B^2$.

If $(e_1,\ldots)$ is an orthonormal basis and $x$ is orthogonal to the $(e_i)$, must $x$ be $0$?

Hermitian operator's eigenvectors are not orthonormal and not complete

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