Inequality of Oppenheim for positive subdefinite matrix and metapositive subdefinite matrix

摘要

In this paper, Oppenheim inequality det(A οB)≥ det A nΠi=1bii is modified further. We give a better lower estimate of Hadamard's product determinant in the form of partitioned matrices. Namely,Oppenheim inequality in the form of partitioned matrices:|det (A οB)|≥ |det(A kοBk) det(A21οB/Bk)|+|det(A οB)det(A/Ak )det(B21-B/Bk)|.