Linear Algebra... Finals approaching.
Prove, or provide a counterexample:
Any set of nonzero mutually orthogonal vectors is independent.
I'm 99% sure it's true.
I'm having a little difficulty proving independence abstractly. I know that, orthogonality of two vectors, (e.g., if
u and
v are column vectors) is defined as
u * v^T = 0. And I suspect I will need to prove it by showing that a matrix made up of the vectors is of full column rank. But, I'm just having difficulty getting there!
Any advice is appreciated.
Thank you!