The singular values of the hadamard product of a positive semidefinite and a skew-symmetric matrix
Roy Mathias · Linear and Multilinear Algebra · 1992
Let σ1(X)≤ · ≤ σN(X)≤0 denote the ordered singular values ofan n × n matrix X and let α1 (X) ≤ α2(X)≤ · ≤ αn(X) denote its ordered main diagonal entries (assuming that they are real). Let B be any complex n × n skew-symmetric matrix and ||.|| any unitarily invariant norm. It is shown that for any rea positive semidefinite n × n matrix A.