Pr. 8. (a) Determine how eigenvalues and eigenvectors of B.[0 A], A' 0 are related to singular values and singular vectors of A E JFNXN. In other words, if A = UEV', then express eigenvalues and eigenvectors of B in terms of components of U, E and V. Hints: Start with some numerical experiments using self-generated A matrices and form a conjecture. The eigenvalues and singular values are intimately related. Keep in mind that B is 2N x 2N . . . . . . :l: - :l: - Think about combining ul- and 1:,- 1n various ways, such as m :l: '01-, [if] , and [i3] . 'l 7. (b) Optional: write a unitary eigendecomposition of B in matrix form. This problem is related to one SVD numerical approach