Question

$A \in M_2(\mathbb{R}^2)$,$\langle x,y \rangle = x^TAy$ is an inner product iff $\alpha > 0, det(A) > 0$

score 2.4k · Answer 1 · 2014-06-01 17:44:11

2.4k

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$A \in M_2(\mathbb{R}^2)$,$\langle x,y \rangle = x^TAy$ is an inner product iff $\alpha > 0, det(A) > 0$

Published on 01 Jun 2014 - 17:44

score 210 · Answer 2 · 2014-06-01 18:24:06

210

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Evaluating $\int_{\mathbb R^n}e^{-\langle Ax,x \rangle}dx$ where $A$ is symmetric and positive definite

Published on 01 Jun 2014 - 18:24

score 4k · Answer 3 · 2014-06-02 04:34:02

4k

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Inner product and linear transformation

Published on 02 Jun 2014 - 4:34

score 4.1k · Answer 4 · 2026-03-25 11:26:01

4.1k

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Isomorphism of inner product spaces

Published on 25 Mar 2026 - 11:26

score 1.1k · Answer 5 · 2014-06-06 15:01:21

1.1k

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Angle between two polynomials

Published on 06 Jun 2014 - 15:01

score 177 · Answer 6 · 2014-06-06 20:58:09

177

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self adjoint transformations and inner product problem

Published on 06 Jun 2014 - 20:58

score 27 · Answer 7 · 2014-06-07 14:27:55

Let $G_1 = \{v_1 + \lambda w_1 | \lambda \in \mathbb{R}\}, G_2 = \{\{v_2 + \mu w_2 \}$ be two skew lines, derive a formula for $d(G_1,G_2)$

score 84 · Answer 8 · 2026-03-26 20:25:45

84

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Using inner product property to determine if operator is an isomorphism.

Published on 26 Mar 2026 - 20:25

score 60 · Answer 9 · 2014-06-10 10:59:56

60

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Norm and InnerProduct Inequality

Published on 10 Jun 2014 - 10:59

score 107 · Answer 10 · 2014-06-10 12:16:20

Let $\langle x,y \rangle = x_1y_1 + 3x_2y_2 + 4x_3y_3 + x_1y_2 + x_2y_1 + x_1y_3 + x_3y_1 + x_2 y_3+x_3y_2$, prove pos. definiteness

score 128 · Answer 11 · 2014-06-10 13:43:35

128

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Calculate the angles between $(1,X),(X,X^2),(X^2,X^3),(X^3,X^4)$ given the inner product $\langle p(x),q(X) \rangle = \int_{-1}^{1} p(X)q(X)dX$

Published on 10 Jun 2014 - 13:43

score 2k · Answer 12 · 2026-03-28 05:29:01

2k

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Dot product in Curvilinear Coordinate Systems

Published on 28 Mar 2026 - 5:29

score 1.5k · Answer 13 · 2014-06-10 18:30:59

1.5k

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Relationship between matrix 2-norm and orthogonal basis of eigenvectors

Published on 10 Jun 2014 - 18:30

score 333 · Answer 14 · 2014-06-11 04:20:27

333

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Showing an inner product space is complete

Published on 11 Jun 2014 - 4:20

score 671 · Answer 15 · 2014-06-11 10:02:29

671

Views

An inequality for inner product space: $\|x-z\|.\|y-t\|\leq \|x-y\|.\|z-t\|+\|y-z\|.\|x-t\|$

Published on 11 Jun 2014 - 10:02

List Question

$A \in M_2(\mathbb{R}^2)$,$\langle x,y \rangle = x^TAy$ is an inner product iff $\alpha > 0, det(A) > 0$

Evaluating $\int_{\mathbb R^n}e^{-\langle Ax,x \rangle}dx$ where $A$ is symmetric and positive definite

Inner product and linear transformation

Isomorphism of inner product spaces

Angle between two polynomials

self adjoint transformations and inner product problem

Let $G_1 = \{v_1 + \lambda w_1 | \lambda \in \mathbb{R}\}, G_2 = \{\{v_2 + \mu w_2 \}$ be two skew lines, derive a formula for $d(G_1,G_2)$

Using inner product property to determine if operator is an isomorphism.

Norm and InnerProduct Inequality

Let $\langle x,y \rangle = x_1y_1 + 3x_2y_2 + 4x_3y_3 + x_1y_2 + x_2y_1 + x_1y_3 + x_3y_1 + x_2 y_3+x_3y_2$, prove pos. definiteness

Calculate the angles between $(1,X),(X,X^2),(X^2,X^3),(X^3,X^4)$ given the inner product $\langle p(x),q(X) \rangle = \int_{-1}^{1} p(X)q(X)dX$

Dot product in Curvilinear Coordinate Systems

Relationship between matrix 2-norm and orthogonal basis of eigenvectors

Showing an inner product space is complete

An inequality for inner product space: $\|x-z\|.\|y-t\|\leq \|x-y\|.\|z-t\|+\|y-z\|.\|x-t\|$

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