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A Determinant Representation for the Distribution of Quadratic Forms in Complex Normal Vectors

✍ Scribed by Hongsheng Gao; Peter J Smith

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
161 KB
Volume
73
Category
Article
ISSN
0047-259X

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✦ Synopsis

Let the column vectors of X: M_N, M<N, be distributed as independent complex normal vectors with the same covariance matrix 7. Then the usual quadratic form in the complex normal vectors is denoted by Z=XLX H 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|.

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