Question

How to prove two function $\phi_m$ and $\phi_n$ are orthogonal?

score 836 · Answer 1 · 2026-03-24 23:53:50

836

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How to prove two function $\phi_m$ and $\phi_n$ are orthogonal?

Published on 24 Mar 2026 - 23:53

score 26 · Answer 2 · 2026-03-14 04:49:54

26

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$x$ is orthogonal to $v_j$ ($j=1,\dots,r$) iff $x\in\text{span}\{v_{r+1},\dots,v_{n}\}$

Published on 14 Mar 2026 - 4:49

score 41 · Answer 3 · 2018-09-14 13:43:45

41

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Inclusion and orthogonality in a vector space

Published on 14 Sep 2018 - 13:43

score 44 · Answer 4 · 2018-09-14 16:44:54

44

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Find an vector orthogonal to a group of vectors

Published on 14 Sep 2018 - 16:44

score 269 · Answer 5 · 2026-03-26 04:35:15

269

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If $V \in \mathbb{R}^{n \times n}$ is an orthogonal matrix, and $V^T e=0$, ($e$ is the ones vector) then is it true $V_m^T e = 0\, \forall \, m<n$?

Published on 26 Mar 2026 - 4:35

score 375 · Answer 6 · 2026-03-24 23:58:03

375

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Find the Fourier-Bessel Series for $f(x)$ With Respect to the Orthogonal Set: How Was $w(x)$ Found?

Published on 24 Mar 2026 - 23:58

score 154 · Answer 7 · 2026-03-25 17:17:17

154

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Proper and affine subspaces

Published on 25 Mar 2026 - 17:17

score 531 · Answer 8 · 2018-09-18 16:58:48

531

Views

Best approximation of vector.

Published on 18 Sep 2018 - 16:58

score 196 · Answer 9 · 2018-09-20 04:42:37

196

Views

Using Gram-Schmidt to Construct orthonormal basis for $\mathbb{C}^{k+1}$ that includes a unit eigenvector of a matrix

Published on 20 Sep 2018 - 4:42

score 99 · Answer 10 · 2018-09-21 18:03:32

99

Views

Showing $P^TP=I_n-\frac1n11^T$ if $\left(\begin{smallmatrix}\frac1{\sqrt n}&\cdots&\frac1{\sqrt n}\\&P\end{smallmatrix}\right)$ is orthogonal

Published on 21 Sep 2018 - 18:03

score 146 · Answer 11 · 2018-09-23 18:05:59

146

Views

Find the projection of a function $f(x)=1$ to a subspace

Published on 23 Sep 2018 - 18:05

score 391 · Answer 12 · 2018-09-24 14:58:59

391

Views

Orthogonal projection and bases

Published on 24 Sep 2018 - 14:58

score 47 · Answer 13 · 2026-03-25 08:12:59

47

Views

Lower bound on a spanning set projecting onto any one dimensional subspace

Published on 25 Mar 2026 - 8:12

score 65 · Answer 14 · 2026-03-26 01:07:55

65

Views

Find all numbers a and b such that the matrix A is orthogonal

Published on 26 Mar 2026 - 1:07

score 1k · Answer 15 · 2018-09-25 07:25:11

1k

Views

Find all vectors in $\mathbb{R}^5$ such that $S$ is an orthogonal set. Express answer as a linear span.

Published on 25 Sep 2018 - 7:25

List Question

How to prove two function $\phi_m$ and $\phi_n$ are orthogonal?

$x$ is orthogonal to $v_j$ ($j=1,\dots,r$) iff $x\in\text{span}\{v_{r+1},\dots,v_{n}\}$

Inclusion and orthogonality in a vector space

Find an vector orthogonal to a group of vectors

If $V \in \mathbb{R}^{n \times n}$ is an orthogonal matrix, and $V^T e=0$, ($e$ is the ones vector) then is it true $V_m^T e = 0\, \forall \, m<n$?

Find the Fourier-Bessel Series for $f(x)$ With Respect to the Orthogonal Set: How Was $w(x)$ Found?

Proper and affine subspaces

Best approximation of vector.

Using Gram-Schmidt to Construct orthonormal basis for $\mathbb{C}^{k+1}$ that includes a unit eigenvector of a matrix

Showing $P^TP=I_n-\frac1n11^T$ if $\left(\begin{smallmatrix}\frac1{\sqrt n}&\cdots&\frac1{\sqrt n}\\&P\end{smallmatrix}\right)$ is orthogonal

Find the projection of a function $f(x)=1$ to a subspace

Orthogonal projection and bases

Lower bound on a spanning set projecting onto any one dimensional subspace

Find all numbers a and b such that the matrix A is orthogonal

Find all vectors in $\mathbb{R}^5$ such that $S$ is an orthogonal set. Express answer as a linear span.

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