List questions from inner-products

Published on 28 May 2020 - 19:56

91

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For any two vectors $v_1$ and $v_2$, $\langle v_1, v_2 \rangle = \langle T (v_1), T (v_2) \rangle$ if $T$ is norm-preserving.

Published on 29 May 2020 - 8:01

1.2k

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What's the relationship between Banach space and inner product space

Published on 03 Apr 2026 - 16:53

431

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projection of a vector onto a vector space

Published on 27 Mar 2026 - 14:56

99

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How to prove that $ \int_0^1 \frac{e^x}{x+1}dx\le \frac e2$ using the inner product.

Published on 30 Mar 2026 - 3:56

108

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Ficken's characterization of inner product spaces.

Published on 31 May 2020 - 5:57

1k

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Riesz Representation Theorem geometric intuition

Published on 25 Mar 2026 - 19:01

37

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Prove $\{X\in S^n_+ | \langle A,X \rangle =a, \langle B,X\rangle =b, \langle C,X\rangle =c\}$ is bounded

Published on 25 Mar 2026 - 11:32

275

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Minimizing the distance to a subspace (orthogonal projection) if a norm is not induced by an inner product

Published on 27 Mar 2026 - 14:52

251

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adjoint transformation intuition

Published on 25 Mar 2026 - 19:00

289

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self-adjoint operator intuition

Published on 25 Mar 2026 - 22:01

791

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unitary operator explanation

Published on 25 Mar 2026 - 16:06

214

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Prove that an operator preserves length if and only if it is orthogonal

Published on 03 Jun 2020 - 17:20

161

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To which values of $a$ is the following an inner product space?

Published on 03 Jun 2020 - 20:27

45

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Is it correct to state that $\langle x(t),x(t)\rangle' = 2\langle x'(t),x(t)\rangle$ for an arbitrary inner product?

Published on 03 Jun 2020 - 21:06

List Question

Determining operator by inner product

For any two vectors $v_1$ and $v_2$, $\langle v_1, v_2 \rangle = \langle T (v_1), T (v_2) \rangle$ if $T$ is norm-preserving.

What's the relationship between Banach space and inner product space

projection of a vector onto a vector space

How to prove that $ \int_0^1 \frac{e^x}{x+1}dx\le \frac e2$ using the inner product.

Ficken's characterization of inner product spaces.

Riesz Representation Theorem geometric intuition

Prove $\{X\in S^n_+ | \langle A,X \rangle =a, \langle B,X\rangle =b, \langle C,X\rangle =c\}$ is bounded

Minimizing the distance to a subspace (orthogonal projection) if a norm is not induced by an inner product

adjoint transformation intuition

self-adjoint operator intuition

unitary operator explanation

Prove that an operator preserves length if and only if it is orthogonal

To which values of $a$ is the following an inner product space?

Is it correct to state that $\langle x(t),x(t)\rangle' = 2\langle x'(t),x(t)\rangle$ for an arbitrary inner product?

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