Linear Algebra: Introduction to Orthonormal Bases

[initrunlevel0]

just preparing for my linear algebra exam tomorrow...:)

[BannedLol4l]

actually you don't need associativity lol. Only the fact that vi dot (cvj) = (cvi) dot vj

But otherwise your videos are pretty awesome!

[BannedLol4l]

To prove that B is Linearly Independent, you have to assume that vi is any LINEAR COMBINATION of the other vectors, then vi dot vi can be proven to be equal to 0 by using scalar product distributivity and associativity and the fact that vi dot vj = 0 for j not equal to i.

This leads to the contradiction that vi = 0 vector, which proves that no vi is a linear combination of the other vectors in B. This is what means that B is a L.I. set.

[BannedLol4l]

Your proof that B is a linearly independent set is incorrect. You proved that no vector can be a scalar multiple times another of the vectors. But B could be a linearly dependent set even then. Take for example the set: (1, 0, 0) (0, 1, 0) and (1, 1, 0).

Here no vector is a multiple of the other, but (1, 1, 0) = (1, 0, 0) + (0, 1, 1) which means B is a L.D. set.

[cbaide100]

u are awesome!

[Strictz]

Great help, thank you. =)

[begmickey]

i love you.

[NOTAVAILALBEMAN]

Great explanation :)

Greetings from Germany

[Z3rk]

You're amazing, this is so much better than my actual linear algebra class lol

[yonifra2]

another bullseye. thanks a lot Sal!

[prolarka]

tareq, use the playlist

[tareqhardan]

great vids,, but if you could put the nxt video as a response,, so we could go thru them in order...

[PPennyZ]

thanks for your videos, they are sososososososososo helpful ..... I love your explaination .. please keep on making videos