Singular values of products of positive operators: AZB and ZAB Original Research Article

Let A and Z be n-by-n matrices. Suppose A greater-or-equal, slanted 0 (positive semi-definite) and Z > 0 with extremal eigenvalues a and b. Then, for given scalars s, t > 0, there exist unitary matrices U and V such thatimage These are sharp inequalities for singular values. More generally, for monotone pairs of positive operators A and B, there exist unitaries U and V such thatimage