Machine Learning, Artificial Intelligence, Mathematics.
these r uᵢ vectors to be orthonormal. So what are the remaining m - r orthogonal eigenvectors for AAᵀ? Since left nullspace of A is orthogonal to the column space, it is very natural to pick them as the remaining eigenvector. (The left nullsapce N(Aᵀ) is the space span by x in Aᵀx=0.) A similar