On the Properties of Accretive-Dissipative Matrices

Let $A$ be a complex $(n\times n)$ matrix, and let $A=B+iC$, $B=B^*$, $C=C^*$ be its Toeplitz decomposition. Then $A$ is said to be (strictly) accretive if $B>0$ and (strictly) dissipative if $C>0$. We study the properties of matrices that satisfy both these conditions, in other words, of accretive-dissipative matrices. In many respects, these matrices behave as numbers in the first quadrant of the complex plane. Some other properties are natural extensions of the corresponding properties of Hermitian positive-definite matrices.