Let be an upper-bidiagonal matrix having a multiple singular value. Prove that must have a zero on either its diagonal or superdiagonal. Is part true for a lower-bidiagonal matrix. Assume that...

Let

be an upper-bidiagonal matrix having a multiple singular value. Prove that

must have a zero on either its diagonal or superdiagonal.

Is part

true for a lower-bidiagonal matrix.

Assume that the diagonal and superdiagonal of a bidiagonal matrix are nonzero. Show that the singular values of the matrix are distinct.