Question

Let $H$ be a Hilbert space, $V≤H$ be closed, $Q:H→V$ be the orthogonal projection, $(e_n)_{n∈ℕ}$ be an ONB of $H$. Is $(Qe_n)_{n∈ℕ}$ an ONB of $V$?

score 64 · Answer 1 · 2016-06-06 19:46:28

64

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Let $H$ be a Hilbert space, $V≤H$ be closed, $Q:H→V$ be the orthogonal projection, $(e_n)_{n∈ℕ}$ be an ONB of $H$. Is $(Qe_n)_{n∈ℕ}$ an ONB of $V$?

Published on 06 Jun 2016 - 19:46

score 245 · Answer 2 · 2016-06-07 02:41:35

245

Views

Riesz Representation Thereom for Polynomials with real coefficients problem

Published on 07 Jun 2016 - 2:41

score 68 · Answer 3 · 2016-06-09 08:55:49

68

Views

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Published on 09 Jun 2016 - 8:55

score 768 · Answer 4 · 2016-06-09 20:35:25

768

Views

Endomorphism is normal and idempotent iff it is an orthogonal projection.

Published on 09 Jun 2016 - 20:35

score 85 · Answer 5 · 2016-06-10 12:14:21

85

Views

How can we compute the square root of an operator of the form $Cv=\sum_{n\in\mathbb N}\langle v,e_n\rangle_Ve_n$?

Published on 10 Jun 2016 - 12:14

score 591 · Answer 6 · 2016-06-12 21:33:16

591

Views

Orthonormal basis with specific norm

Published on 12 Jun 2016 - 21:33

score 216 · Answer 7 · 2026-03-29 11:02:14

216

Views

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Published on 29 Mar 2026 - 11:02

score 615 · Answer 8 · 2016-06-19 01:02:10

615

Views

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Published on 19 Jun 2016 - 1:02

score 89 · Answer 9 · 2026-03-29 17:52:29

89

Views

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Published on 29 Mar 2026 - 17:52

score 11.4k · Answer 10 · 2026-03-29 02:36:09

11.4k

Views

For an orthogonal matrix $Q$, why does $QQ^T = I$?

Published on 29 Mar 2026 - 2:36

score 164 · Answer 11 · 2016-06-20 18:16:41

164

Views

If $ι:U→V$ is a Hilbert-Schmidt embedding and $(v_n)_{n∈ℕ}$ is an orthonormal basis of $V$, then $(ιι^*v_n)_{n∈ℕ}$ is an orthonormal basis of $ιU$

Published on 20 Jun 2016 - 18:16

score 77 · Answer 12 · 2016-06-20 19:45:12

77

Views

If $Tv=\mu v$ for some $\mu>0$, then $v\in\ker(T^{1/2})^\perp$

Published on 20 Jun 2016 - 19:45

score 1.1k · Answer 13 · 2016-06-20 23:21:26

1.1k

Views

Does a orthogonal basis for the span of $S$ always have the same dimension as the basis of $S$

Published on 20 Jun 2016 - 23:21

score 37 · Answer 14 · 2016-06-21 09:31:36

37

Views

Given A $m\times n$, $\{u_1,...,u_n\}$ ON basis of $R^n$, prove eigenvalues aren't negative

Published on 21 Jun 2016 - 9:31

score 422 · Answer 15 · 2026-03-25 21:50:02

422

Views

How is the study of wavelets not just a special case of Fourier analysis?

Published on 25 Mar 2026 - 21:50

List Question

Let $H$ be a Hilbert space, $V≤H$ be closed, $Q:H→V$ be the orthogonal projection, $(e_n)_{n∈ℕ}$ be an ONB of $H$. Is $(Qe_n)_{n∈ℕ}$ an ONB of $V$?

Riesz Representation Thereom for Polynomials with real coefficients problem

Rule for $\langle x,y\rangle$ if we know orthonormal base?

Endomorphism is normal and idempotent iff it is an orthogonal projection.

How can we compute the square root of an operator of the form $Cv=\sum_{n\in\mathbb N}\langle v,e_n\rangle_Ve_n$?

Orthonormal basis with specific norm

the proof of variational principal for the principal eigenvalue (checking orthonormal subset)

Orthonormal set of basis functions in $L^2([a,b])$

Find SVD of $A$

For an orthogonal matrix $Q$, why does $QQ^T = I$?

If $ι:U→V$ is a Hilbert-Schmidt embedding and $(v_n)_{n∈ℕ}$ is an orthonormal basis of $V$, then $(ιι^*v_n)_{n∈ℕ}$ is an orthonormal basis of $ιU$

If $Tv=\mu v$ for some $\mu>0$, then $v\in\ker(T^{1/2})^\perp$

Does a orthogonal basis for the span of $S$ always have the same dimension as the basis of $S$

Given A $m\times n$, $\{u_1,...,u_n\}$ ON basis of $R^n$, prove eigenvalues aren't negative

How is the study of wavelets not just a special case of Fourier analysis?

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