Question

Show that $|\lambda|\leq 1$ for each eigenvalue $\lambda$ of a partial isometry

score 255 · Answer 1 · 2026-04-14 22:27:55

255

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Show that $|\lambda|\leq 1$ for each eigenvalue $\lambda$ of a partial isometry

Published on 14 Apr 2026 - 22:27

score 1.4k · Answer 2 · 2026-04-15 18:46:14

1.4k

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If $A$ is normal, then $A(M)\subset M \Rightarrow A(M^{\perp})\subset M^{\perp}$.

Published on 15 Apr 2026 - 18:46

score 856 · Answer 3 · 2026-04-12 06:41:49

856

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Does Gram-Schmidt always work correctly?

Published on 12 Apr 2026 - 6:41

score 111 · Answer 4 · 2026-04-15 00:10:15

111

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Question regarding positive definiteness decompositions

Published on 15 Apr 2026 - 0:10

score 4.4k · Answer 5 · 2026-04-16 08:09:12

4.4k

Views

Dual space and inner/scalar product space

Published on 16 Apr 2026 - 8:09

score 365 · Answer 6 · 2026-04-15 22:20:03

365

Views

polar decomposition on finite dimensional vector spaces

Published on 15 Apr 2026 - 22:20

score 159 · Answer 7 · 2026-04-13 12:07:08

159

Views

Find the adjoint of this operator.

Published on 13 Apr 2026 - 12:07

score 117 · Answer 8 · 2026-04-16 21:20:05

117

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Given $\langle p,q\rangle = \int_{-1}^{1} {t^2 p(t)q(t)dt}$, find an orthogonal basis for $W$ subspace

Published on 16 Apr 2026 - 21:20

score 104 · Answer 9 · 2026-04-15 20:18:14

104

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In an inner product space over $\mathbb R$, prove $ (u,w)=0 \Leftrightarrow \left \| u+w \right \|=\left \| u-w \right \| $

Published on 15 Apr 2026 - 20:18

score 140 · Answer 10 · 2026-04-13 21:30:11

140

Views

Prove: $\|\lambda v\| = |\lambda| \cdot \|v\| $

Published on 13 Apr 2026 - 21:30

score 173 · Answer 11 · 2026-04-14 03:49:54

173

Views

Prove/disprove the following theories regarding operators in inner product spaces

Published on 14 Apr 2026 - 3:49

score 93 · Answer 12 · 2026-04-15 01:06:50

93

Views

A simple piece of a Lemma on Gram-Schmidt

Published on 15 Apr 2026 - 1:06

score 1.1k · Answer 13 · 2026-04-14 20:13:44

1.1k

Views

Prove an equality between dimensions of kernels

Published on 14 Apr 2026 - 20:13

score 106 · Answer 14 · 2026-04-12 02:56:53

106

Views

find scalar product of vectors in rectangular

Published on 12 Apr 2026 - 2:56

score 2.6k · Answer 15 · 2026-04-12 02:45:43

2.6k

Views

Indefinite inner product spaces?

Published on 12 Apr 2026 - 2:45

List Question

Show that $|\lambda|\leq 1$ for each eigenvalue $\lambda$ of a partial isometry

If $A$ is normal, then $A(M)\subset M \Rightarrow A(M^{\perp})\subset M^{\perp}$.

Does Gram-Schmidt always work correctly?

Question regarding positive definiteness decompositions

Dual space and inner/scalar product space

polar decomposition on finite dimensional vector spaces

Find the adjoint of this operator.

Given $\langle p,q\rangle = \int_{-1}^{1} {t^2 p(t)q(t)dt}$, find an orthogonal basis for $W$ subspace

In an inner product space over $\mathbb R$, prove $ (u,w)=0 \Leftrightarrow \left \| u+w \right \|=\left \| u-w \right \| $

Prove: $\|\lambda v\| = |\lambda| \cdot \|v\| $

Prove/disprove the following theories regarding operators in inner product spaces

A simple piece of a Lemma on Gram-Schmidt

Prove an equality between dimensions of kernels

find scalar product of vectors in rectangular

Indefinite inner product spaces?

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