An Inequality for Positive Semidefinite Hermitian Matrices(1)
Russell Merris · Canadian Mathematical Bulletin · 1974
Let A and B be positive semidefinite Hermitian n-square matrices. If A—B is positive semidefinite, write A≥B. Haynsworth [1] has proved that if A≥B then det(A+B)≥det A+n det B. Let G be a subgroup of the symmetric group, Sn, and let λ be a character on G. Let where A = (aij) and Er is the rth elementary symmetric function.