Question

$V^⊥$ where V is spanned by ${\cos x, \cos^2 x, \cos^3 x, \cos^4 x, . . . }$

score 87 · Answer 1 · 2026-04-14 16:39:12

87

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$V^⊥$ where V is spanned by ${\cos x, \cos^2 x, \cos^3 x, \cos^4 x, . . . }$

Published on 14 Apr 2026 - 16:39

score 1.9k · Answer 2 · 2026-04-12 19:28:50

1.9k

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Finding if the orthonormal basis of P1 with a given inner product

Published on 12 Apr 2026 - 19:28

score 478 · Answer 3 · 2026-04-13 03:22:46

478

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Cauchy-Schwarz for integrals

Published on 13 Apr 2026 - 3:22

score 397 · Answer 4 · 2026-04-14 21:40:27

397

Views

$\int_{A}f^2 = 0$ implies $f(x) = 0 \text{ } \forall x \in A$

Published on 14 Apr 2026 - 21:40

score 880 · Answer 5 · 2026-04-12 14:22:22

880

Views

Is an Infinite Dimensional Inner Product Space Isomorphic to its Continuous Dual Space?

Published on 12 Apr 2026 - 14:22

score 328 · Answer 6 · 2026-04-11 03:34:17

328

Views

Continuity of inner product and change of limit order

Published on 11 Apr 2026 - 3:34

score 127 · Answer 7 · 2026-03-28 09:53:29

127

Views

Let ($\pi, V$) be a representation of $G$ with character $X$: if $\langle X, X\rangle=2$ then $V$ is the sum of two irreducible representations

Published on 28 Mar 2026 - 9:53

score 174 · Answer 8 · 2026-04-16 01:54:40

174

Views

Non singular matrix $M$ such that $MAM^T=F$, normal form

Published on 16 Apr 2026 - 1:54

score 2k · Answer 9 · 2026-04-13 21:32:28

2k

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Prove that, for a closed subspace $W$ of a vector space $V$, $(W^{\perp})^{\perp} = W$

Published on 13 Apr 2026 - 21:32

score 506 · Answer 10 · 2026-03-26 20:44:28

506

Views

Solution to Systems of Equations, Orthogonal Polynomials

Published on 26 Mar 2026 - 20:44

score 2.6k · Answer 11 · 2026-04-14 21:34:53

2.6k

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If $\{u, v\}$ is an orthonormal set, how is $\|u - v\| = \sqrt{2}$?

Published on 14 Apr 2026 - 21:34

score 2.8k · Answer 12 · 2026-04-12 03:42:49

2.8k

Views

Maximizing and minimizing dot products

Published on 12 Apr 2026 - 3:42

score 83 · Answer 13 · 2026-04-14 13:42:57

83

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Find the extrema of $\sum_{i=1}^n u_i v_i \log \left| \frac{v_i}{u_i} \right|$

Published on 14 Apr 2026 - 13:42

score 485 · Answer 14 · 2026-04-14 08:37:32

485

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On the proof of $\langle T(v),v \rangle = 0$ for all $v \in V \iff T(v)=0$ for all $v \in V $

Published on 14 Apr 2026 - 8:37

score 1k · Answer 15 · 2026-03-28 15:36:47

1k

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Is the adjoint of an isometry $S$ the inverse of $S$?

Published on 28 Mar 2026 - 15:36

List Question

$V^⊥$ where V is spanned by ${\cos x, \cos^2 x, \cos^3 x, \cos^4 x, . . . }$

Finding if the orthonormal basis of P1 with a given inner product

Cauchy-Schwarz for integrals

$\int_{A}f^2 = 0$ implies $f(x) = 0 \text{ } \forall x \in A$

Is an Infinite Dimensional Inner Product Space Isomorphic to its Continuous Dual Space?

Continuity of inner product and change of limit order

Let ($\pi, V$) be a representation of $G$ with character $X$: if $\langle X, X\rangle=2$ then $V$ is the sum of two irreducible representations

Non singular matrix $M$ such that $MAM^T=F$, normal form

Prove that, for a closed subspace $W$ of a vector space $V$, $(W^{\perp})^{\perp} = W$

Solution to Systems of Equations, Orthogonal Polynomials

If $\{u, v\}$ is an orthonormal set, how is $\|u - v\| = \sqrt{2}$?

Maximizing and minimizing dot products

Find the extrema of $\sum_{i=1}^n u_i v_i \log \left| \frac{v_i}{u_i} \right|$

On the proof of $\langle T(v),v \rangle = 0$ for all $v \in V \iff T(v)=0$ for all $v \in V $

Is the adjoint of an isometry $S$ the inverse of $S$?

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