List questions from inner-products

Published on 10 Apr 2026 - 17:50

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Existence of a certain inner product

Published on 13 Apr 2026 - 22:12

162

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Is $\langle f \rangle $ an "inner product"?

Published on 15 Apr 2026 - 7:46

711

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Orthogonal Decomposition

Published on 17 Apr 2026 - 10:10

1.2k

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hoffman-and-kunze [chapter 8.2][question 4]

Published on 16 Apr 2026 - 10:20

231

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$90$-degree angle formed by $2$ non-orthogonal complex vectors?

Published on 09 Apr 2026 - 19:21

398

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Two non-zero complex vectors that are perpendicular but NOT orthogonal?

Published on 13 Apr 2026 - 19:11

1.5k

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Prove that the following are not inner products.

Published on 14 Apr 2026 - 4:42

49

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Is there a basis $\beta$ for $V$ such that $\langle \mathbf{v}, \mathbf{w}\rangle=\langle [\mathbf{v}]_{\beta}, [\mathbf{w}]_{\beta}\rangle$.

Published on 16 Apr 2026 - 12:21

274

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A complete orthonormal set in a finite inner product space $X$ is also a basis for $X$

Published on 15 Apr 2026 - 0:15

60

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Proof of the following equality with vectors

Published on 12 Apr 2026 - 7:49

39

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Prove that an orthonormal sublist and a vector in an inner product space is linearly independent.

Published on 14 Apr 2026 - 0:29

97

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Impossible result: linearly dependent orthonormal basis

Published on 14 Apr 2026 - 8:50

410

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Inner product of orthonormal basis vectors and their derivatives.

Published on 13 Apr 2026 - 18:11

137

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Show $\pi$ is the orthogonal projection of $W$ iff $\|\pi(u)\| \leq \|u\|$ for all $u \in V$

Published on 15 Apr 2026 - 13:16

List Question

Is a bra the adjoint of a ket?

Existence of a certain inner product

Is $\langle f \rangle $ an "inner product"?

Orthogonal Decomposition

hoffman-and-kunze [chapter 8.2][question 4]

$90$-degree angle formed by $2$ non-orthogonal complex vectors?

Two non-zero complex vectors that are perpendicular but NOT orthogonal?

Prove that the following are not inner products.

Is there a basis $\beta$ for $V$ such that $\langle \mathbf{v}, \mathbf{w}\rangle=\langle [\mathbf{v}]_{\beta}, [\mathbf{w}]_{\beta}\rangle$.

A complete orthonormal set in a finite inner product space $X$ is also a basis for $X$

Proof of the following equality with vectors

Prove that an orthonormal sublist and a vector in an inner product space is linearly independent.

Impossible result: linearly dependent orthonormal basis

Inner product of orthonormal basis vectors and their derivatives.

Show $\pi$ is the orthogonal projection of $W$ iff $\|\pi(u)\| \leq \|u\|$ for all $u \in V$

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