Reversed determinantal inequalities for accretive-dissipative matrices
Minghua Lin · Mathematical Inequalities & Applications · 2012
A matrix A∈Mn(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 = [ A11 A12 A21 A22 ] be an accretive-dissipative matrix, k and l be the orders of A11 and A22 , respectively, and let m = min{k, l} . It is proved |detA| (4κ) m (1+κ)2m |detA11||detA22|, where κ is the maximum of the condition numbers of B and C . Mathematics subject classification (2010): 15A45, 15A15.