ON BILINEAR FORMS IN NORMAL VARIABLES

A. M. MATHAI

Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, QC, Canada H3A 2K6

(Received July 17, 1991; revised February 5, 1992)

Abstract. Bilinear forms in normal variables when the matrices of the forms are rectangular are considered. Explicit expressions for the cumulants, joint cumulants and joint cumulants of bilinear and quadratic forms are given. Necessary and sufficient conditions are established for the independence of two bilinear forms as well as a bilinear and a quadratic form. Special cases are shown to agree with known results.

Key words and phrases: Bilinear forms, quadratic forms, moments, cumulants, joint cumulants, independence of bilinear and quadratic forms, nonsingular normal variables.