List questions from inner-products

Published on 12 Sep 2023 - 8:44

46

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If $T$ is self-adjoint and $\alpha \in \mathbb{R}$, show that $\alpha \langle Tv,v \rangle \geq -|\alpha| \lVert Tv \rVert \lVert v \rVert$

Published on 26 Mar 2026 - 6:31

22

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Linear algebra object unclear in the theory behind PCA

Published on 08 Apr 2026 - 16:09

184

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What is the adjoint of the curl operator?

Published on 26 Mar 2026 - 17:33

27

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expectation of sum (or square sum) of two matrices which entries are sampled from normal distribution

Published on 01 Apr 2026 - 5:05

24

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Showing that $(XY_n)$ is a Cauchy sequence when $(Y_n)$ is cauchy in space of polynomias.

Published on 01 Apr 2026 - 11:59

101

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If $U$ and $V$ are unit vectors and $U\cdot V=1$, is it true that $U=V$?

Published on 20 Sep 2023 - 15:30

24

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dot product of surface and gradient

Published on 21 Sep 2023 - 12:21

93

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How to understand this equation by linear algebra?

Published on 08 Apr 2026 - 0:14

55

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Mock scalar product's nonlinearity as a derivation

Published on 09 Apr 2026 - 11:20

57

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Show that $(Ker(\psi))^{\perp} \subset Im(\phi)$

Published on 29 Mar 2026 - 12:12

119

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Understanding Matrix Multiplication: Column-Row Decomposition

Published on 09 Apr 2026 - 14:43

66

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The distance in $\mathbb{R}^n$ is not induced by an inner product.

Published on 29 Sep 2023 - 15:55

62

Views

How can I show $\|XMY\|=\|M\|$?

Published on 11 Apr 2026 - 22:57

57

Views

Double orthogonal complement in general finite-dimensional inner product space

Published on 01 Oct 2023 - 20:04

List Question

Any inner product is determined by the lengths of vectors

If $T$ is self-adjoint and $\alpha \in \mathbb{R}$, show that $\alpha \langle Tv,v \rangle \geq -|\alpha| \lVert Tv \rVert \lVert v \rVert$

Linear algebra object unclear in the theory behind PCA

What is the adjoint of the curl operator?

expectation of sum (or square sum) of two matrices which entries are sampled from normal distribution

Showing that $(XY_n)$ is a Cauchy sequence when $(Y_n)$ is cauchy in space of polynomias.

If $U$ and $V$ are unit vectors and $U\cdot V=1$, is it true that $U=V$?

dot product of surface and gradient

How to understand this equation by linear algebra?

Mock scalar product's nonlinearity as a derivation

Show that $(Ker(\psi))^{\perp} \subset Im(\phi)$

Understanding Matrix Multiplication: Column-Row Decomposition

The distance in $\mathbb{R}^n$ is not induced by an inner product.

How can I show $\|XMY\|=\|M\|$?

Double orthogonal complement in general finite-dimensional inner product space

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