Cochran's Theorem, Rank Additivity, and Tripotent Matrices

摘要

Our purpose in this paper is to review various extensions of Cochran's Theorem in a bibliographic and historical perspective, with special emphasis on matrix-theoretic analogues. while we present over 30 references, we note that Scarowsky (1973) has a rather complete discussion and bibliography on the distribution of quadratic forms in normal random variables.