Applied Linear Algebra: QR Decomposition

This lecture focuses on the classic QR decomposition and shows how it is related to the Gram-Schmidt orthogonalization procedure.

[laradavid]

this is honestly one of the best linalg classes ive seen

[yassine]

Thank you Dr Nathan for the great explanation and to the University of Washington for the public sharing of the entire course material for free and this isn't just any course this is the bleeding edge of applied mathematics, SVD, QR, least squares... Thank you again professor

[a.c.]

Best explanation I found so far, thank you!

[behnamhashemi]

Good professor in general of course. I just noted that he did not answer the question in minute 49:00 correctly! To make norm(q_1) equal to one, you would divide a_1 by norm(a_1), not by the square of norm(a_1). So, the correct formula is
q_1 = a_1/norm(a_1).

I guess the professor confused that with dividing by norm(q_1) which is obviously equal to the square of norm(q_1).

[Aravindaan-qf]

Firstly, thanks a lot for this video! I had a quick question: If A is a m*n matrix, then each column of A is a m-dimensional vector. So, how can a set of n m-dimensional vectors form a basis for (or even span) an n-dimensional space unless n=m? The n m-dimensional vectors can only span an m-dimensional space, right? (and even that is possible if and only if we assume n>=m)