Let P = A(A^TA)^-1A^T, where A is an mxn matrix of rank n.
(1) Show that P^2 = P.
(2) Prove P^k = P for K = 1,2,....
(3) Show that P is symmetric.
Let AЄR^(mxn) and let r be a solution to the least square problem Ax=b. Show that a vector yЄR^n will also be a solution if and only if y = r + z, for some vector zЄN(A).© BrainMass Inc. brainmass.com March 4, 2021, 6:03 pm ad1c9bdddf
There are several proofs regarding matrices here, including a proof of a symmetric matrix.