Accession Number : ADA267883


Title :   Closed Form Characteristic Function for General Complex Second-Order Form in Correlated Complex Gaussian Random Variables


Descriptive Note : Progress rept.,


Corporate Author : NAVAL UNDERSEA WARFARE CENTER DIV NEWPORT RI


Personal Author(s) : Nuttall, Albert H


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a267883.pdf


Report Date : 12 Jul 1993


Pagination or Media Count : 65


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.... Characteristic function, Complex form, Second-order form, Correlated variables, Gaussian variables, Closed form.


Descriptors :   *RANDOM VARIABLES , *MATRICES(MATHEMATICS) , *EIGENVECTORS , *CORRELATION , *VARIABLES , FUNCTIONS , APPROXIMATION(MATHEMATICS) , EXPANSION , VALUE , INTEGRAL EQUATIONS , SQUARE ROOTS


Subject Categories : Numerical Mathematics
      Theoretical Mathematics
      Statistics and Probability


Distribution Statement : APPROVED FOR PUBLIC RELEASE