Closed Form Characteristic Function for General Complex Second-Order Form in Correlated Complex Gaussian Random Variables
Abstract
The properties of the left and right eigenvectors of generalized characteristic value 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 12, 1993
- Accession Number
- ADA267737
Entities
People
- Albert H. Nuttall
Organizations
- Naval Undersea Warfare Center