List questions from inner-products

Published on 26 Mar 2026 - 20:41

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Selfadjoint Endomorphism

Published on 29 Mar 2026 - 3:44

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Show $\|A\|=\sup_{x\neq 0} \langle Ax,x\rangle/\langle x,x\rangle$ for a positive operator $A$.

Published on 13 Apr 2026 - 14:09

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Eigenvalues of a particular map $\Bbb C^3 \to \Bbb C^3$ involving an inner product

Published on 16 Apr 2026 - 13:44

171

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Linear Algebra inner products & orthonormal basis

Published on 14 Apr 2026 - 23:47

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Characterization of a projection operator in $\mathbb R^n$

Published on 08 Apr 2026 - 18:47

332

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Determine whether $\langle f, g \rangle = \int_{-1}^1 f'(x) g'(x) \,dx$ is an inner product on $C^1[-1, 1]$

Published on 17 Apr 2026 - 15:59

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Is $|(v,\frac{Pv}{||Pv||})|=||Pv||$ when $P$ is an orthogonal projection?

Published on 12 Apr 2026 - 1:00

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Are $b$ and $c$ linearly dependent if the inner product $a \cdot b = a \cdot c$?

Published on 12 Apr 2026 - 13:21

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Showing that $\{\sin(nx)\}_{n=1}^\infty$ is a complete orthogonal system in $C([0,2\pi])$ and $L_2[0,\pi]$.

Published on 09 Dec 2015 - 15:04

62

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Tricky problem regarding Bilinear Forms,

Published on 12 Apr 2026 - 3:58

654

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Proof for $U^{\perp \perp} =U$.

Published on 13 Apr 2026 - 8:06

7.2k

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Proof for $(U+W)^\perp=U^\perp \cap W^\perp$ if $U$ and $W$ are both subspaces.

Published on 15 Apr 2026 - 13:36

138

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Biliniear form to inner product

Published on 14 Apr 2026 - 7:52

73

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Inner products over fields other than $\mathbb{R}$ or $\mathbb{C}$

Published on 16 Apr 2026 - 20:27

List Question

Calculate orthonormal basis using Gram-Schmidt

Selfadjoint Endomorphism

Show $\|A\|=\sup_{x\neq 0} \langle Ax,x\rangle/\langle x,x\rangle$ for a positive operator $A$.

Eigenvalues of a particular map $\Bbb C^3 \to \Bbb C^3$ involving an inner product

Linear Algebra inner products & orthonormal basis

Characterization of a projection operator in $\mathbb R^n$

Determine whether $\langle f, g \rangle = \int_{-1}^1 f'(x) g'(x) \,dx$ is an inner product on $C^1[-1, 1]$

Is $|(v,\frac{Pv}{||Pv||})|=||Pv||$ when $P$ is an orthogonal projection?

Are $b$ and $c$ linearly dependent if the inner product $a \cdot b = a \cdot c$?

Showing that $\{\sin(nx)\}_{n=1}^\infty$ is a complete orthogonal system in $C([0,2\pi])$ and $L_2[0,\pi]$.

Tricky problem regarding Bilinear Forms,

Proof for $U^{\perp \perp} =U$.

Proof for $(U+W)^\perp=U^\perp \cap W^\perp$ if $U$ and $W$ are both subspaces.

Biliniear form to inner product

Inner products over fields other than $\mathbb{R}$ or $\mathbb{C}$

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