On dissipative matrices Original Research Article

A matrix the imaginary part of whose Toeplitz (Cartesian) decomposition is positive semidefinite [positive definite] is said to be dissipative [strictly dissipative]. Characterizations for strictly dissipative matrices and related theory are given. Dissipative-preserving linear transformations are characterized. Finally, a natural generalization to linear transformations on matrices is developed in terms of the completely positive cone; ten characterizations follow.