List questions from inner-products

Published on 13 Dec 2018 - 22:34

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In $\mathbb{R}^n$, is the dot product the only inner product?

Published on 14 Dec 2018 - 11:02

88

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Cross Products/Determinants/Matrix Multiplication Under Arbitrary Inner Products

Published on 29 Mar 2026 - 7:28

142

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Show that the $L^{p}$ norm $\|f\|_{L^{p}} := \big( \int^{b}_{a} |f(x)|^p\big)^{1/p}$ is not induced by a scalar product for $p \neq 2$.

Published on 29 Mar 2026 - 13:40

224

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Element not orthogonal to any other non zero element

Published on 16 Dec 2018 - 12:08

66

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Proving an inner product

Published on 26 Mar 2026 - 18:59

96

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Basis of an Orthogonal Complement

Published on 26 Mar 2026 - 7:56

172

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Is every normable topological vector space "inner productable"?

Published on 26 Mar 2026 - 6:20

340

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When is a topological vector space “inner product-able”?

Published on 26 Mar 2026 - 6:18

52

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Why convergence of these two series is equivalent?

Published on 28 Mar 2026 - 14:54

41

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Resulting distribution from inner product between vector which entries are normally distributed and another vector

Published on 30 Mar 2026 - 12:25

239

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Cauchy Schwarz inequality for $\langle f,g\rangle = \int_0^1f(x)g(x)\mathrm{d}x$

Published on 20 Dec 2018 - 0:33

112

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Proving that $\langle \textbf {a,b} \rangle = \|\textbf {a}\| \|\textbf {b}\| \cos \theta$.

Published on 20 Dec 2018 - 5:35

82

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Maximize product of a vector with two vectors

Published on 27 Mar 2026 - 16:47

1.2k

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Inner product with orthogonal complement

Published on 26 Mar 2026 - 22:19

List Question

Distance between two polynomials (inner product)

In $\mathbb{R}^n$, is the dot product the only inner product?

Cross Products/Determinants/Matrix Multiplication Under Arbitrary Inner Products

Show that the $L^{p}$ norm $\|f\|_{L^{p}} := \big( \int^{b}_{a} |f(x)|^p\big)^{1/p}$ is not induced by a scalar product for $p \neq 2$.

Element not orthogonal to any other non zero element

Proving an inner product

Basis of an Orthogonal Complement

Is every normable topological vector space "inner productable"?

When is a topological vector space “inner product-able”?

Why convergence of these two series is equivalent?

Resulting distribution from inner product between vector which entries are normally distributed and another vector

Cauchy Schwarz inequality for $\langle f,g\rangle = \int_0^1f(x)g(x)\mathrm{d}x$

Proving that $\langle \textbf {a,b} \rangle = \|\textbf {a}\| \|\textbf {b}\| \cos \theta$.

Maximize product of a vector with two vectors

Inner product with orthogonal complement

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