List questions from inner-products

Published on 13 Apr 2026 - 19:23

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Property of orthogonal projection onto a closed convex set in euclidean $\mathbb{R}^{n}$

Published on 12 Apr 2026 - 14:15

30

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Prove that $R_{\frac{u-v}{|u-v|}}$ sends $u$ to $v$ and $v$ to $u$.

Published on 13 Apr 2026 - 22:24

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$\left \| x+y \right \|^2+\left \| x-y \right \|^2=2\left \| x \right \|^2+2\left \| y \right \|^2$

Published on 17 Apr 2026 - 2:28

401

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If $V$ is a finite dimensional inner product space and $e_n$ an orthonormal basis, for $x\in V$, why is $x=\sum_{k=1}^{n}\langle x,e_k\rangle e_k$?

Published on 16 Apr 2026 - 6:06

688

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Prove that the Triangle Inequality is an equality iff $\langle u,v\rangle=\|u\|\,\|v\|$

Published on 16 Apr 2026 - 14:37

166

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If $x\perp E$ then $x\perp\overline{\operatorname{span}E}.$

Published on 12 Apr 2026 - 5:19

52

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Inequality on inner product which does not involve the norms

Published on 10 Apr 2026 - 18:09

43

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Specific values for scalar product: generalizing orthogonality.

Published on 14 Apr 2026 - 19:01

98

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Zorn's Lemma in the proof of Riesz representation theorem

Published on 13 Apr 2026 - 17:53

1.8k

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Finding the angle a vector makes with the 'horizontal'

Published on 11 Apr 2026 - 6:34

66

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linear algebra norm from inner space

Published on 11 Apr 2026 - 4:41

1.3k

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Relation between Hilbert-Schmidt inner product and tensor products

Published on 11 Apr 2026 - 18:08

247

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A trick in Linear algebra

Published on 12 Apr 2026 - 8:34

175

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Satisfying Conditions for Inner Product in Space $R^2$

Published on 11 Apr 2026 - 22:40

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vectorial functional equation

Property of orthogonal projection onto a closed convex set in euclidean $\mathbb{R}^{n}$

Prove that $R_{\frac{u-v}{|u-v|}}$ sends $u$ to $v$ and $v$ to $u$.

$\left \| x+y \right \|^2+\left \| x-y \right \|^2=2\left \| x \right \|^2+2\left \| y \right \|^2$

If $V$ is a finite dimensional inner product space and $e_n$ an orthonormal basis, for $x\in V$, why is $x=\sum_{k=1}^{n}\langle x,e_k\rangle e_k$?

Prove that the Triangle Inequality is an equality iff $\langle u,v\rangle=\|u\|\,\|v\|$

If $x\perp E$ then $x\perp\overline{\operatorname{span}E}.$

Inequality on inner product which does not involve the norms

Specific values for scalar product: generalizing orthogonality.

Zorn's Lemma in the proof of Riesz representation theorem

Finding the angle a vector makes with the 'horizontal'

linear algebra norm from inner space

Relation between Hilbert-Schmidt inner product and tensor products

A trick in Linear algebra

Satisfying Conditions for Inner Product in Space $R^2$

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