论文信息 - On the Properties of Accretive-Dissipative Matrices

On the Properties of Accretive-Dissipative Matrices

Let A be a complex n × 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.

Alan George | Kh. D. Ikramov | K. Ikramov | A. George

[1] On sectorial matrices , 2003 .

[2] Charles R. Johnson,et al. Uniqueness of matrix square roots and an application , 2001 .

[3] Charles R. Johnson,et al. Topics in Matrix Analysis , 1991 .

[4] M. Neumann,et al. On the square roots of strictly quasiaccretive complex matrices , 1979 .

[5] Compact operators whose real and imaginary parts are positive , 2000 .

[6] Nicholas J. Higham,et al. Factorizing complex symmetric matrices with positive definite real and imaginary parts , 1998, Math. Comput..

[7] Tosio Kato. Perturbation theory for linear operators , 1966 .

[8] Andrey B. Kucherov,et al. Bounding the growth factor in Gaussian elimination for Buckley's class of complex symmetric matrices , 2000 .

[9] Roy Mathias,et al. Matrices with Positive Definite Hermitian Part: Inequalities and Linear Systems , 1992, SIAM J. Matrix Anal. Appl..

[10] Alan George,et al. On the growth factor in Gaussian elimination for generalized Higham matrices , 2002, Numer. Linear Algebra Appl..

[11] Charles R. Johnson,et al. Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[12] R. Bhatia. Matrix Analysis , 1996 .