List questions from orthogonality

Published on 19 Apr 2018 - 18:35

363

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Find orthonormal basis given inner product.

Published on 25 Mar 2026 - 9:47

56

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Orthogonal projection into 2 different closed linear subspaces implies they are equal.

Published on 24 Apr 2018 - 15:26

76

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Find orthogonal complement of given set

Published on 26 Apr 2018 - 16:19

226

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Orthogonality in $N$-dimensional spherical coordinates

Published on 25 Mar 2026 - 2:59

1.3k

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$A(A^T A)^{-1} A^T$ is the matrix of the orthogonal projection to im A

Published on 29 Apr 2018 - 20:29

62

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Why $\sum_nA_n(X_n,X_m)=A_m(X_m,X_m)$?

Published on 25 Mar 2026 - 8:00

393

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Prove that complex exponentials $(\phi_n(x)=\frac{1}{\sqrt{a}}e^{i\frac{2\pi nx}{a}})_{n=0, \pm 1, \pm2,...}$ are complete and orthonormal on $[0,a]$

Published on 01 May 2018 - 8:42

448

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Find an orthogonal basis for ℝ3 that begins with an orthogonal basis for Col()

Published on 25 Mar 2026 - 9:50

574

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Ternary self orthogonal codes have weight divisible by $3$

Published on 25 Mar 2026 - 12:55

93

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Find a basis for $W^\perp$ for $W=\{(x_1,x_2,x_3)\in\mathbb{R}^3:x_1-x_2-x_3=0\}$

Published on 02 May 2018 - 18:11

359

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Form of Lorentz Transformation in 3D space

Published on 20 Mar 2026 - 7:42

59

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Notation with Complex inner product space question

Published on 06 May 2018 - 4:38

265

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Invertibility of blocks in a block orthogonal matrix

Published on 06 May 2018 - 10:10

162

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Ensemble of periodic functions orthogonal to their derivative

Published on 25 Mar 2026 - 11:13

List Question

Orthogonal function in direction of another?

Find orthonormal basis given inner product.

Orthogonal projection into 2 different closed linear subspaces implies they are equal.

Find orthogonal complement of given set

Orthogonality in $N$-dimensional spherical coordinates

$A(A^T A)^{-1} A^T$ is the matrix of the orthogonal projection to im A

Why $\sum_nA_n(X_n,X_m)=A_m(X_m,X_m)$?

Prove that complex exponentials $(\phi_n(x)=\frac{1}{\sqrt{a}}e^{i\frac{2\pi nx}{a}})_{n=0, \pm 1, \pm2,...}$ are complete and orthonormal on $[0,a]$

Find an orthogonal basis for ℝ3 that begins with an orthogonal basis for Col()

Ternary self orthogonal codes have weight divisible by $3$

Find a basis for $W^\perp$ for $W=\{(x_1,x_2,x_3)\in\mathbb{R}^3:x_1-x_2-x_3=0\}$

Form of Lorentz Transformation in 3D space

Notation with Complex inner product space question

Invertibility of blocks in a block orthogonal matrix

Ensemble of periodic functions orthogonal to their derivative

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