Some Results on Matrices with Prescribed Diagonal Elements and Singular Values
Fuk-yum Sing · Canadian Mathematical Bulletin · 1976
Let A be an n × n complex matrix. The singular values of A are the non-negative square-roots of the eigenvalues of A*A. G. N. De Oliviera [4] gave a necessary condition for the existence of a matrix A with a1..., an as diagonal elements and α1,..., αn as singular values. We shall give another necessary condition which implies the above author’s condition and we show that this is also a sufficient condition for the case n =2.