title: Principal Component Analysis and determinant of the total scatter matrix
body: <p>Hi guys I'm reading a paper Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection, I'm wondering why in PCA the projection W is chosen to maximize the <strong>determinant</strong> of the total scatter matrix of the projected samples, i.e., arg max|W^T S_T W|(in latex form) where S_T is the scatter matrix of the original dataset.
  Thanks very much!</p>