Question

If $(U,〈\;⋅\;,\;⋅\;〉),H$ are Hilbert spaces, $W\in U$, $Y\in H$, $Z\in L(U, H)$ and $f\in L(H,L(H,\mathbb R))$, then $〈Y,fZW〉=〈ZW,fY〉$

score 37 · Answer 1 · 2026-03-29 07:28:55

37

Views

If $(U,〈\;⋅\;,\;⋅\;〉),H$ are Hilbert spaces, $W\in U$, $Y\in H$, $Z\in L(U, H)$ and $f\in L(H,L(H,\mathbb R))$, then $〈Y,fZW〉=〈ZW,fY〉$

Published on 29 Mar 2026 - 7:28

score 1.3k · Answer 2 · 2026-04-13 20:14:05

1.3k

Views

Finding the orbits of the orthogonal group $O(n)$ on $\Bbb R^n$

Published on 13 Apr 2026 - 20:14

score 147 · Answer 3 · 2026-04-13 21:58:54

147

Views

Definition of inner product space

Published on 13 Apr 2026 - 21:58

score 112 · Answer 4 · 2026-04-15 12:37:31

112

Views

$\langle x+y,x-y\rangle=0$

Published on 15 Apr 2026 - 12:37

score 54 · Answer 5 · 2026-04-12 04:17:43

54

Views

How to calculate $\langle v,w\rangle$ based only on $\langle v,x_i\rangle$ and $\langle w,x_i\rangle$?

Published on 12 Apr 2026 - 4:17

score 5.4k · Answer 6 · 2026-04-11 17:38:35

5.4k

Views

Inner product of continuous functions

Published on 11 Apr 2026 - 17:38

score 823 · Answer 7 · 2026-04-14 23:13:34

823

Views

Positive definiteness of a bilinear form implies symmetry?

Published on 14 Apr 2026 - 23:13

score 243 · Answer 8 · 2026-03-30 03:19:15

243

Views

Finding a maximal orthogonal basis from a set of functions

Published on 30 Mar 2026 - 3:19

score 75 · Answer 9 · 2026-04-13 11:33:33

75

Views

Adjoint of linear transformation $T: \mathbb{M_n(C)} \rightarrow \mathbb{M_n(C)}$

Published on 13 Apr 2026 - 11:33

score 197 · Answer 10 · 2026-04-12 01:41:53

197

Views

If $Ax = O$ has only one solutions, the columns of A span R?

Published on 12 Apr 2026 - 1:41

score 4.7k · Answer 11 · 2026-04-14 20:04:27

4.7k

Views

multiplication of finite sum (inner product space)

Published on 14 Apr 2026 - 20:04

score 283 · Answer 12 · 2026-04-16 13:10:32

In a finite dimensional inner product space with $T ∈ L(V)$, show that $\langle u,v\rangle = \langle T(u),T(v)\rangle$ implies $T$ is invertible.

score 2.2k · Answer 13 · 2026-04-15 08:33:09

2.2k

Views

Subspace of Inner product space is an Inner product space

Published on 15 Apr 2026 - 8:33

score 1.5k · Answer 14 · 2026-04-14 12:14:24

1.5k

Views

Is $\langle A,B\rangle =\operatorname{trace}(AB^T)$ an inner product in $\mathbb R^{n\times m}$?

Published on 14 Apr 2026 - 12:14

score 30.2k · Answer 15 · 2026-04-16 18:47:03

30.2k

Views

Proof: Sum of dimension of orthogonal complement and vector subspace

Published on 16 Apr 2026 - 18:47

List Question

If $(U,〈\;⋅\;,\;⋅\;〉),H$ are Hilbert spaces, $W\in U$, $Y\in H$, $Z\in L(U, H)$ and $f\in L(H,L(H,\mathbb R))$, then $〈Y,fZW〉=〈ZW,fY〉$

Finding the orbits of the orthogonal group $O(n)$ on $\Bbb R^n$

Definition of inner product space

$\langle x+y,x-y\rangle=0$

How to calculate $\langle v,w\rangle$ based only on $\langle v,x_i\rangle$ and $\langle w,x_i\rangle$?

Inner product of continuous functions

Positive definiteness of a bilinear form implies symmetry?

Finding a maximal orthogonal basis from a set of functions

Adjoint of linear transformation $T: \mathbb{M_n(C)} \rightarrow \mathbb{M_n(C)}$

If $Ax = O$ has only one solutions, the columns of A span R?

multiplication of finite sum (inner product space)

In a finite dimensional inner product space with $T ∈ L(V)$, show that $\langle u,v\rangle = \langle T(u),T(v)\rangle$ implies $T$ is invertible.

Subspace of Inner product space is an Inner product space

Is $\langle A,B\rangle =\operatorname{trace}(AB^T)$ an inner product in $\mathbb R^{n\times m}$?

Proof: Sum of dimension of orthogonal complement and vector subspace

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