A Determinant Representation for the Distribution of Quadratic Forms in Complex Normal Vectors
- Gao, Hongsheng
- Smith, Peter J
View in ORKG Publication date
May 2000
DOI Publisher
Academic Press. ISSN
0047-259X Citation count (estimate)
39Abstract
AbstractLet the column vectors of X::M×N, M<N, be distributed as independent complex normal vectors with the same covariance matrix Σ. Then the usual quadratic form in the complex normal vectors is denoted by Z=XLXH where L:N×N is a positive definite hermitian matrix. This paper deals with a representation for the density function of Z in terms of a ratio of determinants. This representation also yields a compact form for the distribution of the generalized variance |Z|