Question

Is $C([0,1])$ complete if $\int_{0}^{1} f(x)g(x)dx$ is the inner product?

score 293 · Answer 1 · 2026-04-15 16:35:04

293

Views

Is $C([0,1])$ complete if $\int_{0}^{1} f(x)g(x)dx$ is the inner product?

Published on 15 Apr 2026 - 16:35

score 96 · Answer 2 · 2026-04-17 14:06:39

96

Views

If $A^*= A$ and $A^m= 0$, then $A= 0$.

Published on 17 Apr 2026 - 14:06

score 61 · Answer 3 · 2026-04-17 12:18:11

61

Views

Prove that an orthonormal set $\{y_1,y_2,y_3,\dots\}$ is an orthonormal basis iff $\sum_{m=1}^\infty \vert(y_m,x_n)\vert^2=1\forall n\in \mathbb N$

Published on 17 Apr 2026 - 12:18

score 61 · Answer 4 · 2026-04-15 14:12:13

61

Views

The geometric interpretation of a mapping that projects a vector on to a non-orthogonal basis

Published on 15 Apr 2026 - 14:12

score 85 · Answer 5 · 2026-04-14 05:02:14

85

Views

hermitian inner product that is invariant on a Lie Group

Published on 14 Apr 2026 - 5:02

score 64 · Answer 6 · 2026-04-12 17:40:34

64

Views

Projection of a function $f$ in a Hilbert space $\mathcal{H}$ on a subspace $\mathcal{D}\subset\mathcal{H}$

Published on 12 Apr 2026 - 17:40

score 89 · Answer 7 · 2026-04-16 05:00:29

89

Views

Determine the formula and uniqueness of an inner product for a given orthonormal basis

Published on 16 Apr 2026 - 5:00

score 79 · Answer 8 · 2026-04-12 09:34:14

79

Views

Need help in understanding the proof of <x,y> = $\hat{x}^T A \hat{y}$?

Published on 12 Apr 2026 - 9:34

score 46 · Answer 9 · 2026-04-11 23:15:58

46

Views

Is T Self Adjoint?Is T Bounded?

Published on 11 Apr 2026 - 23:15

score 148 · Answer 10 · 2026-04-11 11:42:15

148

Views

What is wrong in this inner product proof?

Published on 11 Apr 2026 - 11:42

score 91 · Answer 11 · 2026-04-10 14:45:22

91

Views

Relationship between the Lie bracket, inner product, and orthogonality for Matrix Lie algebras?

Published on 10 Apr 2026 - 14:45

score 99 · Answer 12 · 2026-04-13 20:45:28

99

Views

On exact sequences of finite-dimensional inner product spaces

Published on 13 Apr 2026 - 20:45

score 42 · Answer 13 · 2026-04-11 23:34:43

42

Views

Help in question, Inner product space.

Published on 11 Apr 2026 - 23:34

score 121 · Answer 14 · 2026-04-08 18:40:49

121

Views

Are all positive operators Hermitian?

Published on 08 Apr 2026 - 18:40

score 52 · Answer 15 · 2026-04-15 23:09:26

52

Views

Orthogonal bases and Gram–Schmidt

Published on 15 Apr 2026 - 23:09

List Question

Is $C([0,1])$ complete if $\int_{0}^{1} f(x)g(x)dx$ is the inner product?

If $A^*= A$ and $A^m= 0$, then $A= 0$.

Prove that an orthonormal set $\{y_1,y_2,y_3,\dots\}$ is an orthonormal basis iff $\sum_{m=1}^\infty \vert(y_m,x_n)\vert^2=1\forall n\in \mathbb N$

The geometric interpretation of a mapping that projects a vector on to a non-orthogonal basis

hermitian inner product that is invariant on a Lie Group

Projection of a function $f$ in a Hilbert space $\mathcal{H}$ on a subspace $\mathcal{D}\subset\mathcal{H}$

Determine the formula and uniqueness of an inner product for a given orthonormal basis

Need help in understanding the proof of <x,y> = $\hat{x}^T A \hat{y}$?

Is T Self Adjoint?Is T Bounded?

What is wrong in this inner product proof?

Relationship between the Lie bracket, inner product, and orthogonality for Matrix Lie algebras?

On exact sequences of finite-dimensional inner product spaces

Help in question, Inner product space.

Are all positive operators Hermitian?

Orthogonal bases and Gram–Schmidt

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