Summary
Least square solution
Algorithm for finding least square solution
least square may have a general solution
Least square by QR factorization
is already in REF making it easier to solve
Projection
Concept
Least square solution
- solution that is closer than every other vector
Orthogonal projection
Projection is unique
QR factorization
Application
Linear regression
constructing the matrix equation
Extra
Octave
octave
# Least squares solution(last column)
rref([A'*A A'*b])
# Least squares solution if A is QR factorizable
[Q, R] = qr(A)
rref([R Q’*b])