Non-Zero Orthogonal Vectors: Show m<=n

Context: Graduate
Thread starter squenshl
Start date Apr 18, 2009
Tags

Orthogonal Vectors

Join the discussion

Registration is free. Ask a follow-up in this thread, or start your own.

1 reply · 2K views

squenshl

Thread starter
Apr 18, 2009

I need some direction.
Suppose that{u1,u2,...,um} are non-zero pairwise orthogonal vectors (i.e., uj.ui=0 if i doesnt=j) of a subspace W of dimension n. Show that m<=n.

Discussion

Physics news on Phys.org

Ultracold neutrons don't disappear into the mirror world
New research shows how 'hot electrons' can reshape metals in billionths of a second
A way to read quantum bits faster and with less hardware

earlh

Apr 18, 2009

Dude, you already posted a thread like 2 days ago!

https://www.physicsforums.com/showthread.php?t=306934

Non-Zero Orthogonal Vectors: Show m<=n

Discussion

Undergrad The vector to which a dual vector corresponds

Undergrad Spinor calculus

Undergrad Matrix representation of rank-2 spinors

Undergrad Looking for a paper about spinors

Undergrad Why are these cycles disjoint and of equal length?

On the Moore–Penrose inverse from a banal linear algebra viewpoint

Undergrad Correct constructed example of Abelian Monoid?

Undergrad Correct state row entries in the following Sequential machine?

Insights Why Vector Spaces Explain The World: A Historical Perspective

Undergrad Quintic Polynomial Tschirnhaus Transform: Possible complex Bring Radicals

Insights Revisiting the Velocity-Time Function

Insights Remote Operated Gate Control System

Insights AI Enriched Problem Solving

Insights Thinking Outside The Box Versus Knowing What’s In The Box

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

Non-Zero Orthogonal Vectors: Show m<=n

Discussion

Similar threads

Graduate Suppose that{u1,u2, ,um} are non-zero pairwise orthogonal vectors

Prove mutually non-zero orthogonal vectors are linearly independent