Closed Form Characteristic Function for General Complex Second-Order Form inCorrelated Complex Gaussian Random Variables

摘要

The properties of the left and right eigenvectors of generalized characteristicvalue problems with non-Hermitian complex matrices are reviewed, and diagonal expansions of various matrix combinations and inverses are derived. The interrelationships of the solutions of two related non-Hermitian characteristic value problems are determined and found to be simply related to the earlier eigenvectors and their properties. These results are then applied to the evaluation of the characteristic function of a general complex second-order form in correlated Gaussian random variables. The end result is a compact closed form result involving a finite product and a finite sum, along with one square root and exponential. This expression allows for rapid evaluation of the characteristic function for numerous values of its complex argument.... Characteristic function, Complex form, Second-order form, Correlated variables, Gaussian variables, Closed form.