Question

Explanation of the orthogonality relation $\int_{-π}^{π}\sin(ax)\sin(bx)\,dx=\int_{-π}^{π}\cos(ax)\cos(bx)\,dx=\begin{cases}π,&a=b\\0,&a≠b\end{cases}$

score 409 · Answer 1 · 2020-04-23 14:43:43

409

Views

Explanation of the orthogonality relation $\int_{-π}^{π}\sin(ax)\sin(bx)\,dx=\int_{-π}^{π}\cos(ax)\cos(bx)\,dx=\begin{cases}π,&a=b\\0,&a≠b\end{cases}$

Published on 23 Apr 2020 - 14:43

score 438 · Answer 2 · 2026-03-27 10:10:02

438

Views

Question about the proof that the orthogonal complement of the kernel is the image of the adjoint

Published on 27 Mar 2026 - 10:10

score 348 · Answer 3 · 2026-03-25 09:26:11

348

Views

Orthonormalization of basis - Diagonalization of overlap matrix.

Published on 25 Mar 2026 - 9:26

score 129 · Answer 4 · 2020-04-26 14:17:39

129

Views

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Published on 26 Apr 2020 - 14:17

score 51 · Answer 5 · 2020-04-26 17:23:32

51

Views

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score 1.1k · Answer 6 · 2026-03-28 01:46:08

1.1k

Views

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Published on 28 Mar 2026 - 1:46

score 956 · Answer 7 · 2026-03-27 07:50:35

956

Views

Prove T is an isometry if and only if ${T(e_1),T(e_2),\cdots T(e_n)}$ forms an orthonormal basis of $R^n$

Published on 27 Mar 2026 - 7:50

score 38 · Answer 8 · 2020-04-29 05:33:47

38

Views

Orthogonal complements are same implies subspaces are same

Published on 29 Apr 2020 - 5:33

score 78 · Answer 9 · 2020-04-30 15:31:14

78

Views

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score 91 · Answer 10 · 2026-03-25 14:25:17

91

Views

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Published on 25 Mar 2026 - 14:25

score 523 · Answer 11 · 2020-05-01 17:28:57

523

Views

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Published on 01 May 2020 - 17:28

score 471 · Answer 12 · 2026-03-29 05:58:42

471

Views

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Published on 29 Mar 2026 - 5:58

score 41 · Answer 13 · 2020-05-03 18:35:40

41

Views

If $U$ is spanned by $e_1,\ldots,e_k$ and $V$ is a subspace with $U^\perp\cap V=\emptyset$, then $v=e_k+w$ for some $v\in V$ and $w\in U^\perp$

Published on 03 May 2020 - 18:35

score 268 · Answer 14 · 2026-02-23 00:47:41

268

Views

A question involving Self Polar Orthogonality

Published on 23 Feb 2026 - 0:47

score 569 · Answer 15 · 2026-03-27 01:46:29

569

Views

Orthogonal Projections Are Symmetric - Geometric Intuition

Published on 27 Mar 2026 - 1:46

List Question

Explanation of the orthogonality relation $\int_{-π}^{π}\sin(ax)\sin(bx)\,dx=\int_{-π}^{π}\cos(ax)\cos(bx)\,dx=\begin{cases}π,&a=b\\0,&a≠b\end{cases}$

Question about the proof that the orthogonal complement of the kernel is the image of the adjoint

Orthonormalization of basis - Diagonalization of overlap matrix.

Find double orthogonal complement of non-empty subset of Hilbert space

Orthogonality Condition

How can I extend a set to an orthogonal basis?

Prove T is an isometry if and only if ${T(e_1),T(e_2),\cdots T(e_n)}$ forms an orthonormal basis of $R^n$

Orthogonal complements are same implies subspaces are same

Find elements $f,g$ of the orthogonal Lie_Algebra with $f \circ g \neq 0$

$(n-1)$-Hausdorff measure of orthogonal projection onto an hyperplane of compact sets of $\Bbb R^n$

Does Orthogonality imply linear independence always? if not a counter example

Desmos help - making a finite length line with origin on a sine wave move along it and vary angle orthogonal to sine wave line

If $U$ is spanned by $e_1,\ldots,e_k$ and $V$ is a subspace with $U^\perp\cap V=\emptyset$, then $v=e_k+w$ for some $v\in V$ and $w\in U^\perp$

A question involving Self Polar Orthogonality

Orthogonal Projections Are Symmetric - Geometric Intuition

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