List questions from orthonormal

Published on 22 Mar 2026 - 14:34

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What is $\| f \|$ where $f(x)=\sum\limits_{n=1}^\infty \frac{1}{3^n} \langle x,e_n\rangle$

Published on 22 Mar 2026 - 15:42

159

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Forming an orthonormal basis with these independent vectors

Published on 24 Mar 2026 - 3:31

391

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Orthogonal Function Dirac Delta Series

Published on 24 Mar 2026 - 7:58

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Sum of two rank $1$ matrices with some property gives rank $2$ matrix

Published on 22 Mar 2026 - 21:25

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Zero element in an Hilbert space is orthogonal?

Published on 23 Mar 2026 - 7:13

125

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Prove that $\lVert X\rVert^2 =\sum_{i,j=1}^\infty\lvert\langle u_i,Xu_j\rangle\rvert^2$.

Published on 25 Mar 2026 - 1:24

109

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Is there any connection between the fact that a set of vectors are mutually orthogonal and the same set of vectors are linearly independent

Published on 25 Mar 2026 - 2:02

133

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Compute the norm of a linear operator using a normal basis in an infinite Hilbert space

Published on 22 Mar 2026 - 22:32

688

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If $M$ is the span of a finite orthonormal set in a Hilbert space then $M$ is closed

Published on 23 Mar 2026 - 6:23

509

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Complete orthonormal system in P2(R)

Published on 22 Mar 2026 - 14:01

74

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Spectral Theorem for bounded selfadjoint operators

Published on 22 Mar 2026 - 4:42

212

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Gram-Schmidt orthonormal basis

Published on 25 Mar 2026 - 4:24

311

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Unitary Matrix and Orthonormal Basis

Published on 24 Mar 2026 - 20:36

268

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Matrices and Unit Circle on an Orthonormal Basis

Published on 24 Mar 2026 - 20:36

List Question

Orthonormal basis for $L^2(\mathbb{R}^n,\mathbb{F})$

What is $\| f \|$ where $f(x)=\sum\limits_{n=1}^\infty \frac{1}{3^n} \langle x,e_n\rangle$

Forming an orthonormal basis with these independent vectors

Orthogonal Function Dirac Delta Series

Sum of two rank $1$ matrices with some property gives rank $2$ matrix

Zero element in an Hilbert space is orthogonal?

Prove that $\lVert X\rVert^2 =\sum_{i,j=1}^\infty\lvert\langle u_i,Xu_j\rangle\rvert^2$.

Is there any connection between the fact that a set of vectors are mutually orthogonal and the same set of vectors are linearly independent

Compute the norm of a linear operator using a normal basis in an infinite Hilbert space

If $M$ is the span of a finite orthonormal set in a Hilbert space then $M$ is closed

Complete orthonormal system in P2(R)

Spectral Theorem for bounded selfadjoint operators

Gram-Schmidt orthonormal basis

Unitary Matrix and Orthonormal Basis

Matrices and Unit Circle on an Orthonormal Basis

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