Abstract
A parallel flats fraction (PFF) for an s n factorial experiment, when s is a prime or prime power, is defined as the set of all solutions over GF( s) to At = c i , i = 1, 2, …, f where A is r × n of rank r. The fraction is completely determined by A and C = [ c 1, c 2, …, c f ]; hence all optimality conditions are also completely determined by A and C. It has been shown before that for s a prime the information matrix for a parallel flats fraction can be characterized in terms of the direct sum of relatively small matrices over the cyclotomic field of order s over the rationals. In this paper for s a prime we obtain the eigenvalues (the spectrum) of the information matrix and the eigenvectors directly in terms of these smaller matrices over the cyclotomic field. The usefulness of these results are in the construction of optimal fractions and the comparison of competing fractions.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call