Abstract
Let A, B, P, Q be n-square nonsingular complex matrices, and for 1 ⩽ m < n let U and V be n× m complex matrices. For n⩾3 necessary and sufficient conditions are given for the inequality det(U ∗AV) det(V ∗BU)⩽ det(U ∗PU) det(V ∗QV) to hold for all U and V.
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