Let x denote the real n-tuple (x1,…,xn), (xx… ) the iterated n-tuple (x1,…,xn,x1,…xn…), A = (a i j) and A' a square matrix and its transpose. We wish to consider the effect of nonsingular transformations on a sum x(A1, + ... + Ak)x' of k quadratic forms when the real symmetric matrices Ai and A = A, + ... + Ak are subjected to certain restrictions on their ranks. The results attained link a theorem in statistics with a theorem in ring theory (see Corollary 3). Extension of the results to hermitean forms follows easily.
Proceedings of the Iowa Academy of Science
© Copyright 1948 by the Iowa Academy of Science, Inc.
"Simultaneous Reduction of Quadratic Forms,"
Proceedings of the Iowa Academy of Science: Vol. 55:
, Article 39.
Available at: https://scholarworks.uni.edu/pias/vol55/iss1/39