List questions from inner-products

Published on 14 Apr 2026 - 17:30

932

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Inner product for dual space

Published on 11 Apr 2026 - 20:24

62

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Is my proof correct (normal operator)?

Published on 10 Apr 2026 - 15:42

518

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Prove that if $V$ and $W$ are orthogonal subspaces, then $V \cap W=\{0\}$

Published on 16 Apr 2026 - 5:38

503

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If $\langle x,y\rangle = \langle x,z\rangle$ , then $y=z$ PROOF

Published on 13 Apr 2026 - 5:58

302

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Separation of a convex set and a vector by a hyperplane

Published on 12 Apr 2026 - 1:00

2k

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Finding the orthogonal projection of a given vector on the given subspace W of the inner product space V.

Published on 14 Apr 2026 - 14:45

89

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Show that $\langle y_i, y_j\rangle = 0 \forall i \neq j.$

Published on 15 Apr 2026 - 6:02

801

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Let $V$ be an inner product space. Prove $\langle x, 0\rangle = \langle 0, x\rangle = 0$ for $x \in V$.

Published on 15 Apr 2026 - 19:18

1.9k

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Prove that $R(T^{*})^\perp =N(T)$

Published on 29 Mar 2026 - 5:35

80

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How can there be an inner product space when inner product yields a scalar?

Published on 11 Apr 2026 - 19:47

124

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How do I prove that $\left \langle T(x),x \right \rangle=0,\forall x\in V\Rightarrow T=T_0$?

Published on 14 Apr 2026 - 15:04

205

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A conjugate LT in an inner product space

Published on 15 Apr 2026 - 3:45

12.8k

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Why does the Cauchy-Schwarz Inequality even have a name?

Published on 16 Apr 2026 - 15:24

159

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the complement subspace of a subspace of an ips

Published on 14 Apr 2026 - 5:13

List Question

Generalized inner product

Inner product for dual space

Is my proof correct (normal operator)?

Prove that if $V$ and $W$ are orthogonal subspaces, then $V \cap W=\{0\}$

If $\langle x,y\rangle = \langle x,z\rangle$ , then $y=z$ PROOF

Separation of a convex set and a vector by a hyperplane

Finding the orthogonal projection of a given vector on the given subspace W of the inner product space V.

Show that $\langle y_i, y_j\rangle = 0 \forall i \neq j.$

Let $V$ be an inner product space. Prove $\langle x, 0\rangle = \langle 0, x\rangle = 0$ for $x \in V$.

Prove that $R(T^{*})^\perp =N(T)$

How can there be an inner product space when inner product yields a scalar?

How do I prove that $\left \langle T(x),x \right \rangle=0,\forall x\in V\Rightarrow T=T_0$?

A conjugate LT in an inner product space

Why does the Cauchy-Schwarz Inequality even have a name?

the complement subspace of a subspace of an ips

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