List questions from orthonormal

Published on 07 Sep 2016 - 14:28

125

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How to prove that $(x − y) \perp y$?

Published on 22 Sep 2016 - 11:03

323

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How to write the vector $(1,1,1)$ as a linear combination of an orthonormal basis.

Published on 23 Sep 2016 - 5:05

100

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Why is $l^2$ space needed in definition of weighted shift?

Published on 25 Sep 2016 - 17:00

98

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How to find an orthonormal base from a base?

Published on 02 Oct 2016 - 5:13

44

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Proving a difficult inequality involving orthonormal vectors of $\mathbb{R}^4$

Published on 26 Mar 2026 - 21:25

18.9k

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Getting a transformation matrix from a normal vector

Published on 06 Oct 2016 - 15:31

11.3k

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The need for the Gram–Schmidt process

Published on 25 Mar 2026 - 14:21

43

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Given an ONB $(v_n)_{n∈ℕ}$ of a closed subspace $V$ of a Hilbert space $U$, can we supplement $(v_n)_{n∈ℕ}$ to an ONB of $U$ by elements of $V^⊥$?

Published on 25 Mar 2026 - 6:30

1.4k

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Find all the points where the tangent plane is perpendicular to a given vector.

Published on 17 Oct 2016 - 21:36

112

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Does $L^2(M)$ always admit a basis of nowhere-vanishing functions?

Published on 22 Oct 2016 - 5:11

4.9k

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Uniqueness of orthonormal basis

Published on 25 Mar 2026 - 12:53

155

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Show that for any $x,y \in X$, $\sum_{k=1}^\infty|\left<x,e_k\right>\left<y,e_k\right>|\le \|x\|\|y\|.$

Published on 02 Nov 2016 - 22:52

328

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Prove that a sequence is orthogonal in a Hilbert space

Published on 07 Nov 2016 - 20:14

2.9k

Views

How to show a set is orthogonal

Published on 12 Nov 2016 - 22:14

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Doubt about Inner Product

How to prove that $(x − y) \perp y$?

How to write the vector $(1,1,1)$ as a linear combination of an orthonormal basis.

Why is $l^2$ space needed in definition of weighted shift?

How to find an orthonormal base from a base?

Proving a difficult inequality involving orthonormal vectors of $\mathbb{R}^4$

Getting a transformation matrix from a normal vector

The need for the Gram–Schmidt process

Given an ONB $(v_n)_{n∈ℕ}$ of a closed subspace $V$ of a Hilbert space $U$, can we supplement $(v_n)_{n∈ℕ}$ to an ONB of $U$ by elements of $V^⊥$?

Find all the points where the tangent plane is perpendicular to a given vector.

Does $L^2(M)$ always admit a basis of nowhere-vanishing functions?

Uniqueness of orthonormal basis

Show that for any $x,y \in X$, $\sum_{k=1}^\infty|\left<x,e_k\right>\left<y,e_k\right>|\le \|x\|\|y\|.$

Prove that a sequence is orthogonal in a Hilbert space

How to show a set is orthogonal

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