A note on the proportion of singular (0, 1)-matrices in a class associated with fractional 2n factorial designs |
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Authors: | J.S Huang B.L Raktoe |
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Affiliation: | Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada |
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Abstract: | Let the set T = {(x1, x2,…, xn): xi = 0, 1}. Since the elements of T can be seen as binary representations of integers, we order them with their corresponding integer values. Let be the set of (n + 1) × (n + 1) matrices of the form [1 … D], where the n + 1 rows of D are distinct ordered elements of T. We show that the proportion of singular matrices in approaches 0 as n → ∞. |
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