Questions.txt

Q1: Why does the matrix P^T P have a zero eigenvalue? 
 
Because the rank of P^T P is at most N-1 (where N is the number of images), so there are fewer non-zero eigenvalues than the matrix size. This happens because the images are linearly dependent after subtracting the mean.


Q2: Why is the matrix P P^T symmetric?

Because P P^T equals its transpose, (P P^T)^T = P P^T. This is a property of matrix multiplication for covariance-like matrices.