Handbook of Linear Algebra, 2nd Edition

Chapter 44

D-Optimal Matrices

Michael G. Neubauer

California State University, Northridge

William Watkins

California State University, Northridge

An m × n matrix W whose entries are all 1 or −1 is called a (±1)-design matrix; if the entries of W are 0 or 1, then W is a (0, 1)-design matrix. Each design matrix corresponds to a weighing design; that is, a scheme for estimating the weights of n objects in m weighings. Since the weights of n objects cannot be estimated in fewer than n weighings, we consider only those pairs (m, n) with m ≥ n. The rows of W encode a two-pan or one-pan weighing design with n objects x1, ...,xn being weighed in m weighings. If W ∈ {±1}m × n, an entry of 1 in the (i,j)-th position of W indicates that object xj is put ...