Question

A visual proof:A projection $T$ is orthogonal if $||Tx||\leq ||x||$, $x\in V$.

score 1.2k · Answer 1 · 2026-03-26 09:42:50

1.2k

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A visual proof:A projection $T$ is orthogonal if $||Tx||\leq ||x||$, $x\in V$.

Published on 26 Mar 2026 - 9:42

score 12 · Answer 2 · 2026-02-27 17:53:05

12

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Question about an identity on the squared norm of differences as sum of real parts of inner products

Published on 27 Feb 2026 - 17:53

score 1.1k · Answer 3 · 2020-04-06 04:16:04

1.1k

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$V$ is a vector space with inner product $( , )$. If $(v,w)=0$ for all $v$ belongs to $V$, show that $w=0$.

Published on 06 Apr 2020 - 4:16

score 49 · Answer 4 · 2020-04-08 01:27:27

49

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$\rho(v) = \lambda v$, $\rho(v') = \lambda ' v'$ where $\lambda ' \neq \lambda\Rightarrow \langle v,v'\rangle = 0$

Published on 08 Apr 2020 - 1:27

score 23 · Answer 5 · 2020-04-08 09:59:23

23

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Definition of $F\leq G$ $F,G\in B(H)$ in Hilbert Space

Published on 08 Apr 2020 - 9:59

score 444 · Answer 6 · 2026-03-27 07:17:03

444

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If $p$ and $q$ are orthogonal projections in $\mathbb{R}^n$, then $\Vert p(x)- q(x)\Vert\leq \Vert x\Vert$

Published on 27 Mar 2026 - 7:17

score 35 · Answer 7 · 2026-03-29 20:51:55

35

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sign of inner product of linear independent vectors

Published on 29 Mar 2026 - 20:51

score 46 · Answer 8 · 2020-04-09 18:16:29

46

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Why is this inner product equal to $0$?

Published on 09 Apr 2020 - 18:16

score 35 · Answer 9 · 2026-03-29 02:31:23

35

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What can we say about, $b=\langle x^TA,x \rangle$?

Published on 29 Mar 2026 - 2:31

score 395 · Answer 10 · 2020-04-09 21:28:36

395

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Is there an absolute notion of length on a vector space?

Published on 09 Apr 2020 - 21:28

score 28 · Answer 11 · 2026-03-26 17:31:33

28

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Proving $||f-S_nf||_2 \rightarrow 0$ as $n \rightarrow \infty$

Published on 26 Mar 2026 - 17:31

score 144 · Answer 12 · 2020-04-14 20:42:28

144

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What properties must a field $K$ satisfy in order to define an inner product on a $K\!$-vector space?

Published on 14 Apr 2020 - 20:42

score 893 · Answer 13 · 2026-03-26 14:19:39

893

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Can Hilbert spaces be defined over fields other than $\mathbb R$ and $\mathbb C$?

Published on 26 Mar 2026 - 14:19

score 324 · Answer 14 · 2020-04-15 13:07:50

324

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Positive operator and inner product

Published on 15 Apr 2020 - 13:07

score 189 · Answer 15 · 2020-04-16 01:49:25

189

Views

How do I expand an inner product of a matrix?

Published on 16 Apr 2020 - 1:49

List Question

A visual proof:A projection $T$ is orthogonal if $||Tx||\leq ||x||$, $x\in V$.

Question about an identity on the squared norm of differences as sum of real parts of inner products

$V$ is a vector space with inner product $( , )$. If $(v,w)=0$ for all $v$ belongs to $V$, show that $w=0$.

$\rho(v) = \lambda v$, $\rho(v') = \lambda ' v'$ where $\lambda ' \neq \lambda\Rightarrow \langle v,v'\rangle = 0$

Definition of $F\leq G$ $F,G\in B(H)$ in Hilbert Space

If $p$ and $q$ are orthogonal projections in $\mathbb{R}^n$, then $\Vert p(x)- q(x)\Vert\leq \Vert x\Vert$

sign of inner product of linear independent vectors

Why is this inner product equal to $0$?

What can we say about, $b=\langle x^TA,x \rangle$?

Is there an absolute notion of length on a vector space?

Proving $||f-S_nf||_2 \rightarrow 0$ as $n \rightarrow \infty$

What properties must a field $K$ satisfy in order to define an inner product on a $K\!$-vector space?

Can Hilbert spaces be defined over fields other than $\mathbb R$ and $\mathbb C$?

Positive operator and inner product

How do I expand an inner product of a matrix?

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