List questions from inner-products

Published on 17 Apr 2026 - 3:32

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An example when $(U^\perp)^\perp = U$ but $V\ne U\oplus U^\perp$?

Published on 12 Apr 2026 - 3:13

177

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Exercise $5$, Section $6.A$ - Linear Algebra Done Right

Published on 16 Apr 2026 - 13:53

385

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Find inner product associated with norm

Published on 14 Apr 2026 - 21:04

338

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Time complexity of inner product of two vectors of polynomials

Published on 18 Apr 2026 - 18:24

47

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For $\alpha_1,\alpha_2,\cdots,\alpha_m$ in a $R$-vector space, can there exist $\alpha$ such that $(\alpha,\alpha_i)>0,\forall 1\le i\le m$?

Published on 17 Apr 2026 - 1:36

48

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Inner product of two Schwartz fucntions.

Published on 14 Apr 2026 - 9:22

54

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Polar form of hermitian products

Published on 14 Apr 2026 - 6:21

1.7k

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What is convolution, how does it relate to inner product?

Published on 13 Apr 2026 - 12:18

62

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Inner Product Space $X$ with $x,y \in X$, ${\lVert y \rVert} = 1$, solve for $\lambda \in \mathbb{C}$ that minimizes ${\lVert x - \lambda y \rVert}$

Published on 16 Apr 2026 - 1:20

114

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Intuition of different products of tensor

Published on 09 Apr 2026 - 22:04

180

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Let $U,W$ be finite-dimensional subspaces. Prove that $P_U P_W =0$ if and only if $\langle u,w\rangle = 0$ for all $u\in U, w\in W.$

Published on 15 Apr 2026 - 19:17

116

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Collection of all unitary operators in a Hilbert space is a closed set

Published on 14 Apr 2026 - 15:36

55

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Find an ortonormal base for the subespace $S$ of $\mathbb{C}^3$ span by the vectors $v_1=(1,0,i)$ and $v_2=(2,1,1+i)$

Published on 15 Apr 2026 - 16:21

61

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Is congruency same as $*$-congruency for real matrices?

Published on 12 Apr 2026 - 14:22

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Matrix singular value decomposition

An example when $(U^\perp)^\perp = U$ but $V\ne U\oplus U^\perp$?

Exercise $5$, Section $6.A$ - Linear Algebra Done Right

Find inner product associated with norm

Time complexity of inner product of two vectors of polynomials

For $\alpha_1,\alpha_2,\cdots,\alpha_m$ in a $R$-vector space, can there exist $\alpha$ such that $(\alpha,\alpha_i)>0,\forall 1\le i\le m$?

Inner product of two Schwartz fucntions.

Polar form of hermitian products

What is convolution, how does it relate to inner product?

Inner Product Space $X$ with $x,y \in X$, ${\lVert y \rVert} = 1$, solve for $\lambda \in \mathbb{C}$ that minimizes ${\lVert x - \lambda y \rVert}$

Intuition of different products of tensor

Let $U,W$ be finite-dimensional subspaces. Prove that $P_U P_W =0$ if and only if $\langle u,w\rangle = 0$ for all $u\in U, w\in W.$

Collection of all unitary operators in a Hilbert space is a closed set

Find an ortonormal base for the subespace $S$ of $\mathbb{C}^3$ span by the vectors $v_1=(1,0,i)$ and $v_2=(2,1,1+i)$

Is congruency same as $*$-congruency for real matrices?

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