REVERSED DETERMINANTAL INEQUALITIES FOR ACCRETIVE-DISSIPATIVE MATRICES

A matrix A is an element of 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 = [GRAPHICS] be an accretive-dissipative matrix, k and l be the orders of A(11) and A(22), respectively, and let m = min{k, l}. It is proved vertical bar detA vertical bar >= (4 kappa)(m)/(1+kappa)(2m) vertical bar det A(11)vertical bar vertical bar det A(22)vertical bar, where kappa is the maximum of the condition numbers of B and C.