Prove that $\overline{\mathrm{span}\lbrace x_k\rbrace_{k=1}^\infty}=\ell^2$ where $x_k := (0, ..., \underset{\text{k-th spot}}{1/\sqrt k}, 0, 0,...,)$

score 75 · Answer 9 · 2022-10-16 13:49:13

75

Views

Proving this operator is bounded and then calculating $||T||$ and $||T^*||$.

Published on 16 Oct 2022 - 13:49

score 51 · Answer 10 · 2026-03-26 14:25:10

51

Views

Completing a set of orthonormal vectors in $\mathbb{R}^n$

Published on 26 Mar 2026 - 14:25

score 94 · Answer 11 · 2026-03-26 14:20:34

94

Views

Dimensions of non square matrix?

Published on 26 Mar 2026 - 14:20

score 148 · Answer 12 · 2026-04-01 02:46:43

148

Views

Using orthogonal basis to solve lineal regression

Published on 01 Apr 2026 - 2:46

score 52 · Answer 13 · 2022-10-29 12:25:50

52

Views

Find an ortonormal base for the subespace $S$ of $\mathbb{C}^3$ span by the vectors $v_1=(1,0,i)$ and $v_2=(2,1,1+i)$

Published on 29 Oct 2022 - 12:25

score 121 · Answer 14 · 2022-10-30 19:27:38

121

Views

Can the usual Fourier series of a function be viewed as that defined with respect to an orthonormal system of functions?

Published on 30 Oct 2022 - 19:27

score 129 · Answer 15 · 2022-11-03 17:22:20

129

Views

Showing given linear functional on Hilbert Space is not continuous.

Published on 03 Nov 2022 - 17:22

List Question

Finding and visualising orthonormal basis

Linear combination of vectors that yields two orthonormal vectors.

Orthonormal sequence $L^2[0,1]$ (Brezis 5.30)

Get Vector between unit vectors at certain angle in 3d

Proof of equivalence of two definitions of an orthonormal basis on a Hilbert space

$D=U^TAU$ A is symmetric positive semi-definite

Non-square orthogonal matrix $B$ with $B^TB=I$

Prove that $\overline{\mathrm{span}\lbrace x_k\rbrace_{k=1}^\infty}=\ell^2$ where $x_k := (0, ..., \underset{\text{k-th spot}}{1/\sqrt k}, 0, 0,...,)$

Proving this operator is bounded and then calculating $||T||$ and $||T^*||$.

Completing a set of orthonormal vectors in $\mathbb{R}^n$

Dimensions of non square matrix?

Using orthogonal basis to solve lineal regression

Find an ortonormal base for the subespace $S$ of $\mathbb{C}^3$ span by the vectors $v_1=(1,0,i)$ and $v_2=(2,1,1+i)$

Can the usual Fourier series of a function be viewed as that defined with respect to an orthonormal system of functions?

Showing given linear functional on Hilbert Space is not continuous.

Trending Questions

Popular # Hahtags

Popular Questions