Question

Maximize $ax + by + cz$ given $x^2 + y^2 + z^2 = k^2$. Write answer as Schwartz inequality for dot products.

score 91 · Answer 1 · 2014-10-06 02:44:22

91

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Maximize $ax + by + cz$ given $x^2 + y^2 + z^2 = k^2$. Write answer as Schwartz inequality for dot products.

Published on 06 Oct 2014 - 2:44

score 87 · Answer 2 · 2014-10-06 03:07:53

87

Views

Why is $||v||$ defined as $\sqrt{\langle v, v \rangle}$ and not just $\langle v, v \rangle$?

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score 141 · Answer 3 · 2026-03-25 09:48:40

141

Views

Orthonormal Basis for $[5,1+t]^{\perp}$

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514

Views

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score 46 · Answer 5 · 2014-10-14 19:05:13

46

Views

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2.7k

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score 146 · Answer 7 · 2026-03-26 17:42:28

146

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score 3.1k · Answer 8 · 2014-10-16 15:16:21

3.1k

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119

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score 37 · Answer 10 · 2014-10-17 15:23:00

37

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468

Views

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score 1.6k · Answer 12 · 2014-10-20 02:50:25

1.6k

Views

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Published on 20 Oct 2014 - 2:50

score 112 · Answer 13 · 2026-03-29 05:11:39

112

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score 124 · Answer 14 · 2014-10-22 21:19:36

124

Views

Is it true that $V$ and $V^*$ are naturally isomorphic as finite vector spaces if $V$ is equipped with an inner product?

Published on 22 Oct 2014 - 21:19

score 574 · Answer 15 · 2014-10-23 06:10:05

574

Views

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Published on 23 Oct 2014 - 6:10

List Question

Maximize $ax + by + cz$ given $x^2 + y^2 + z^2 = k^2$. Write answer as Schwartz inequality for dot products.

Why is $||v||$ defined as $\sqrt{\langle v, v \rangle}$ and not just $\langle v, v \rangle$?

Orthonormal Basis for $[5,1+t]^{\perp}$

Gradient of an Inner Product in a more general Vector Space

Is it possible to find the norm fuction of a space from an inner product already defined for it?

Orthogonal direct sum decomposition and projections

Finiteness of the Supremum of Inner Product of Two Finite Sum Positive Sequence

Does every vector space have an inner product?

Finding the maximum of an integral of a function with given constraints.

A question involving inner product on a Hilbert Space

Is $\|x\| = \| \overline{x} \|$ in an inner product space?

Derivative involving inner product

Coordinates of a vector under a basis in a Hilbert space?

Is it true that $V$ and $V^*$ are naturally isomorphic as finite vector spaces if $V$ is equipped with an inner product?

Association of a vector space to metric, normed and inner product spaces

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