Question

Let $T:\mathbb{P_2\to R}$ be transformation. Find basis for kernel of $T$ that is orthogonal w. r. t. inner product. $⟨f(x),g(x)⟩=\int_0^1f(x)g(x)dx$

score 62 · Answer 1 · 2026-04-15 18:22:43

62

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Let $T:\mathbb{P_2\to R}$ be transformation. Find basis for kernel of $T$ that is orthogonal w. r. t. inner product. $⟨f(x),g(x)⟩=\int_0^1f(x)g(x)dx$

Published on 15 Apr 2026 - 18:22

score 653 · Answer 2 · 2026-04-11 23:08:05

653

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Proving a linear transformation that preserves the inner product is an isometry

Published on 11 Apr 2026 - 23:08

score 67 · Answer 3 · 2026-04-17 04:35:07

67

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Proving $\sup\limits_{\theta,\psi}\{||e^{i\theta}x+e^{i\psi}y||^2:\theta,\psi\in \Bbb R\}=||x||^2+||y||^2+2 Re<x,y>$ where $x,y \in \mathbb{C}^n$

Published on 17 Apr 2026 - 4:35

score 45 · Answer 4 · 2026-04-11 23:05:57

45

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About the inner product and the gradient

Published on 11 Apr 2026 - 23:05

score 825 · Answer 5 · 2026-04-13 17:43:18

825

Views

Scalar Triple Product proof

Published on 13 Apr 2026 - 17:43

score 217 · Answer 6 · 2026-04-14 16:29:41

217

Views

Given that the two vectors 8a -b and 4a +3b are perpendicular and that |a |= 2|b |, determine the angle between a and b.

Published on 14 Apr 2026 - 16:29

score 98 · Answer 7 · 2026-04-15 23:24:43

98

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Find inner product

Published on 15 Apr 2026 - 23:24

score 101 · Answer 8 · 2026-04-16 22:44:34

101

Views

Prove that $T = cU$, where c is a scalar and $U$ is unitary.

Published on 16 Apr 2026 - 22:44

score 79 · Answer 9 · 2026-04-14 00:00:07

79

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Doubt from the proof that the sequence space $l^2$ is a Hilbert space from Kreszig book

Published on 14 Apr 2026 - 0:00

score 63 · Answer 10 · 2026-04-14 11:34:39

63

Views

What is $\langle x, \varphi \rangle \overline{\langle x, \varphi \rangle}$ equal to?

Published on 14 Apr 2026 - 11:34

score 39 · Answer 11 · 2026-04-14 22:57:05

39

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The norm and the Fourier coefficient if the inner product $\langle f(x), f(x)\rangle$ is negative.

Published on 14 Apr 2026 - 22:57

score 59 · Answer 12 · 2026-04-13 04:50:54

59

Views

A matrix with inner product that respects norm is a reflection matrix

Published on 13 Apr 2026 - 4:50

score 61 · Answer 13 · 2026-04-13 08:18:02

61

Views

Is there a equivalent norm on $L^p$ induced by inner product?

Published on 13 Apr 2026 - 8:18

score 115 · Answer 14 · 2026-04-10 16:40:03

115

Views

The miraculous nature of the "matrix coefficients" $\langle Tv,v \rangle$ (especially in the context of positive type functions)

Published on 10 Apr 2026 - 16:40

score 88 · Answer 15 · 2026-04-12 13:37:55

88

Views

Show that $\|v\|=\sup \{|\langle v,w \rangle|, \|w\|\leq 1\}$

Published on 12 Apr 2026 - 13:37

List Question

Let $T:\mathbb{P_2\to R}$ be transformation. Find basis for kernel of $T$ that is orthogonal w. r. t. inner product. $⟨f(x),g(x)⟩=\int_0^1f(x)g(x)dx$

Proving a linear transformation that preserves the inner product is an isometry

Proving $\sup\limits_{\theta,\psi}\{||e^{i\theta}x+e^{i\psi}y||^2:\theta,\psi\in \Bbb R\}=||x||^2+||y||^2+2 Re<x,y>$ where $x,y \in \mathbb{C}^n$

About the inner product and the gradient

Scalar Triple Product proof

Given that the two vectors 8a -b and 4a +3b are perpendicular and that |a |= 2|b |, determine the angle between a and b.

Find inner product

Prove that $T = cU$, where c is a scalar and $U$ is unitary.

Doubt from the proof that the sequence space $l^2$ is a Hilbert space from Kreszig book

What is $\langle x, \varphi \rangle \overline{\langle x, \varphi \rangle}$ equal to?

The norm and the Fourier coefficient if the inner product $\langle f(x), f(x)\rangle$ is negative.

A matrix with inner product that respects norm is a reflection matrix

Is there a equivalent norm on $L^p$ induced by inner product?

The miraculous nature of the "matrix coefficients" $\langle Tv,v \rangle$ (especially in the context of positive type functions)

Show that $\|v\|=\sup \{|\langle v,w \rangle|, \|w\|\leq 1\}$

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