Question

Zero element in an Hilbert space is orthogonal?

score 1.1k · Answer 1 · 2026-04-29 12:42:54

1.1k

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Zero element in an Hilbert space is orthogonal?

Published on 29 Apr 2026 - 12:42

score 66 · Answer 2 · 2026-04-29 12:43:06

66

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Proving vectors are orthogonal

Published on 29 Apr 2026 - 12:43

score 63 · Answer 3 · 2026-04-29 12:43:14

63

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$(a\vec{x}+b\vec{v})$ and $(b\vec{x}+a\vec{v})$ are orthogonal. How would you show that $\vec{x}=\vec{0}=\vec{v}$

Published on 29 Apr 2026 - 12:43

score 848 · Answer 4 · 2026-04-29 12:43:13

848

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Orthogonal Trajectories in Differential Equations

Published on 29 Apr 2026 - 12:43

score 158 · Answer 5 · 2026-04-29 12:43:01

if $\vec{x},\vec{y} \in \Bbb{R^4}$ with $\vec{x},\vec{y}$ being linearly independent prove that there exists a $\vec{a}$ that is orthogonal to both?

score 236 · Answer 6 · 2026-04-29 12:43:08

236

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Gradient of an implicit surface at points not on the surface (clarification)

Published on 29 Apr 2026 - 12:43

score 651 · Answer 7 · 2026-04-29 12:43:01

651

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Is the union of the two given sets linearly independent?

Published on 29 Apr 2026 - 12:43

score 51 · Answer 8 · 2026-04-29 12:43:11

51

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Orthogonal projection $P_{W_1}P_{W_2} = P_{W_2}P_{W_1}\iff W_1\perp W_2$

Published on 29 Apr 2026 - 12:43

score 105 · Answer 9 · 2026-05-10 12:30:17

105

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Geometric Intuition for Adding Projections

Published on 10 May 2026 - 12:30

score 94 · Answer 10 · 2026-04-29 12:43:09

94

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If $\|u+\lambda v\| \ge \|u\| \forall \lambda$ then $u \perp v$

Published on 29 Apr 2026 - 12:43

score 294 · Answer 11 · 2026-04-29 12:43:02

294

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If $\dim (\operatorname{Ker}f)^{\perp} = 1$ then $f$ is continuous for $f$ linear functional on Hilbert space

Published on 29 Apr 2026 - 12:43

score 118 · Answer 12 · 2026-04-29 12:42:50

118

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Is there any connection between the fact that a set of vectors are mutually orthogonal and the same set of vectors are linearly independent

Published on 29 Apr 2026 - 12:42

score 477 · Answer 13 · 2026-05-07 10:06:39

477

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Either a self-adjoint operator has $n$ eigenvector or not at all

Published on 07 May 2026 - 10:06

score 2.2k · Answer 14 · 2026-04-29 12:42:59

2.2k

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Prove that if two vectors are orthogonal to another vector, then they are scalar multiples of each other

Published on 29 Apr 2026 - 12:42

score 1k · Answer 15 · 2026-04-29 12:43:06

1k

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Linear-Algebra - How to find a position vector of a point S on a plane, that is also perpendicular to the plane

Published on 29 Apr 2026 - 12:43

List Question

Zero element in an Hilbert space is orthogonal?

Proving vectors are orthogonal

$(a\vec{x}+b\vec{v})$ and $(b\vec{x}+a\vec{v})$ are orthogonal. How would you show that $\vec{x}=\vec{0}=\vec{v}$

Orthogonal Trajectories in Differential Equations

if $\vec{x},\vec{y} \in \Bbb{R^4}$ with $\vec{x},\vec{y}$ being linearly independent prove that there exists a $\vec{a}$ that is orthogonal to both?

Gradient of an implicit surface at points not on the surface (clarification)

Is the union of the two given sets linearly independent?

Orthogonal projection $P_{W_1}P_{W_2} = P_{W_2}P_{W_1}\iff W_1\perp W_2$

Geometric Intuition for Adding Projections

If $\|u+\lambda v\| \ge \|u\| \forall \lambda$ then $u \perp v$

If $\dim (\operatorname{Ker}f)^{\perp} = 1$ then $f$ is continuous for $f$ linear functional on Hilbert space

Is there any connection between the fact that a set of vectors are mutually orthogonal and the same set of vectors are linearly independent

Either a self-adjoint operator has $n$ eigenvector or not at all

Prove that if two vectors are orthogonal to another vector, then they are scalar multiples of each other

Linear-Algebra - How to find a position vector of a point S on a plane, that is also perpendicular to the plane

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