Question

Proof about inner product space $\vert \langle x,y\rangle \vert=\Vert x \Vert\Vert y \Vert$

score 647 · Answer 1 · 2026-03-29 14:02:12

647

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Proof about inner product space $\vert \langle x,y\rangle \vert=\Vert x \Vert\Vert y \Vert$

Published on 29 Mar 2026 - 14:02

score 249 · Answer 2 · 2026-03-25 03:22:18

249

Views

Given a closed, convex, full-dimensional cone $K$, how do I show that $u\in int(K) \iff u^tx>0 \quad \forall x\in K^*-\{0\}$?

Published on 25 Mar 2026 - 3:22

score 211 · Answer 3 · 2026-03-26 18:40:58

211

Views

Proof of cross product and dot product relationship?

Published on 26 Mar 2026 - 18:40

score 51 · Answer 4 · 2026-03-28 20:56:52

51

Views

maps in $L^2(X,\mu, \mathbb{H}) $

Published on 28 Mar 2026 - 20:56

score 398 · Answer 5 · 2020-03-04 18:41:26

398

Views

Let $\{v_1,v_2,...,v_k\}$ be an orthogonal set in $V$. Prove that $\|\sum_{i=1}^k a_i v_i\|^2 = \sum_{i=1}^k |a_i|^2 \|v_i\|^2$.

Published on 04 Mar 2020 - 18:41

score 871 · Answer 6 · 2020-03-05 22:54:12

871

Views

find the orthogonal projection of 1

Published on 05 Mar 2020 - 22:54

score 292 · Answer 7 · 2026-03-25 07:41:45

292

Views

Gram-Schimidt process(trying to understand the projection operator)

Published on 25 Mar 2026 - 7:41

score 59 · Answer 8 · 2020-03-06 04:29:02

59

Views

About theorem of an inner product space, need help on geometric interpretation

Published on 06 Mar 2020 - 4:29

score 1.1k · Answer 9 · 2020-03-06 04:36:58

Question about a problem of inner product space (prove that there exists $y \in V$ such that $y \in W^\perp$, but $\langle x, y \rangle\not= 0$)

score 56 · Answer 10 · 2026-02-23 04:59:05

56

Views

About some $\mathbb R$-algebra morphisms $h:\mathbb C\rightarrow \operatorname{End}_{\mathbb R}(V)$ where $V$ is a symplectic space

Published on 23 Feb 2026 - 4:59

score 119 · Answer 11 · 2026-04-05 17:01:21

119

Views

inner product space proving $S_0 \subseteq S$ implies that $S^{\bot} \subseteq S_0^{\bot}$

Published on 05 Apr 2026 - 17:01

score 102 · Answer 12 · 2020-03-07 03:34:31

102

Views

How does an inequality with respect to norms indicate linear independence?

Published on 07 Mar 2020 - 3:34

score 458 · Answer 13 · 2026-02-23 02:56:52

458

Views

Orthonormal basis and prove $\langle\phi_\beta(x), \phi_\beta(y)\rangle'=\langle[x]_\beta, [y]_\beta\rangle' = \langle x,y\rangle$

Published on 23 Feb 2026 - 2:56

score 39 · Answer 14 · 2020-03-07 21:51:20

39

Views

About a property of inner product space

Published on 07 Mar 2020 - 21:51

score 30 · Answer 15 · 2020-03-07 22:18:53

30

Views

Theorem about coordinates of a subspace in an inner product space

Published on 07 Mar 2020 - 22:18

List Question

Proof about inner product space $\vert \langle x,y\rangle \vert=\Vert x \Vert\Vert y \Vert$

Given a closed, convex, full-dimensional cone $K$, how do I show that $u\in int(K) \iff u^tx>0 \quad \forall x\in K^*-\{0\}$?

Proof of cross product and dot product relationship?

maps in $L^2(X,\mu, \mathbb{H}) $

Let $\{v_1,v_2,...,v_k\}$ be an orthogonal set in $V$. Prove that $\|\sum_{i=1}^k a_i v_i\|^2 = \sum_{i=1}^k |a_i|^2 \|v_i\|^2$.

find the orthogonal projection of 1

Gram-Schimidt process(trying to understand the projection operator)

About theorem of an inner product space, need help on geometric interpretation

Question about a problem of inner product space (prove that there exists $y \in V$ such that $y \in W^\perp$, but $\langle x, y \rangle\not= 0$)

About some $\mathbb R$-algebra morphisms $h:\mathbb C\rightarrow \operatorname{End}_{\mathbb R}(V)$ where $V$ is a symplectic space

inner product space proving $S_0 \subseteq S$ implies that $S^{\bot} \subseteq S_0^{\bot}$

How does an inequality with respect to norms indicate linear independence?

Orthonormal basis and prove $\langle\phi_\beta(x), \phi_\beta(y)\rangle'=\langle[x]_\beta, [y]_\beta\rangle' = \langle x,y\rangle$

About a property of inner product space

Theorem about coordinates of a subspace in an inner product space

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