00:01
Okay, so we have a set of vectors that we're told are non -zero vectors and they're orthogonal.
00:09
Okay, so orthogonal means that if i take u sub n, take the dot product of u sub n with u sub m, that equals zero whenever n is not equal to m.
00:33
So if i take two different vectors and take their dot product, it's gonna be zero.
00:38
That's the definition of an orthogonal set, okay? so we wanna show that they're linearly independent.
00:45
So the test for linear independence is this.
00:49
I write down a summation with some constants a sub n times u n, and i set that equal to zero.
01:07
And if all of the a sub ns are zero, it's the only solution, then they're linearly independent, okay? so all i gotta do is take this thing and dot it with u bar m, pick some one of those as an n.
01:53
And because of my definition of orthogonality, the only term that's left over is, so we have zero is equal to this.
02:04
The only term that's left over is the term where m equals n...