Question

When a projection matrix projects onto the column space of a matrix A, I do not understand why I-P projects onto the left null space. Can someone explain why?

Answer 1

Could you kindly clarify what you mean by left null space? and I-P?

I just watched lecture 15 because my school teaches terribly, and i think i understand it quite well.

Answer 2

Never find. I think I understand it. The left null space is perpendicular to the column space. Since (I-P) dot P gives us 0, I-P projects onto the left null space. The left null space is the nullspace of A(transpose). I is the identity matrix and P is the projection matrix.

Answer 3

Good to hear, i think i'm in over my head too =x. They cover content here i don't see in school.

Answer 4

Same, I have an exam next week and I'm trying to understand everything. The lectures at my school suck as well.