Q):

For convenience, we assume throughout that E is nonsingular Since is symmetric, it has n real eigenvalues A1, ... , and n corresponding orthogonal eigenvectors 111 , 112, ... , un Further, since E is positive definite, the eigenvalues are all positive 12... , n Thus, we have ui u, /\z-ui, > O, i O for every i j Without loss of generality assume that the ui vectors are unit vectors The first set of equations can be rewritten in the matrix form where u and A is a diagonal matrix with diagonal elements