REVERSED DETERMINANTAL INEQUALITIES FOR ACCRETIVE-DISSIPATIVE MATRICES

摘要

A matrix A ∈ M_n (C) is said to be accretive-dissipative if, in its Toeplitz decomposition A = B + iC, B = B*, C = C*, both matrices B and C are positive definite. Let A = [_(A21)~ (A11) _(A22~(A12)] be an accretive-dissipative matrix, k and I be the orders of A_(11) and A22, respectively, and let m = min{k,l}. It is proved |detA|≥(4k)~m/(1+k)~(2m)|detAn||detA_(22)|,where K is the maximum of the condition numbers of B and C.