VARIATIONS ON A THEOREM OF RYSER

A famous theorem of Ryser asserts that a v x v zero-one matrix A satis fying AA(T) = (k - lambda)I + lambda J with k not equal lambda must sa tisfy k + (v - 1)lambda = k(2) and A(T)A = (k - lambda)I + lambda J; s uch a matrix A is called the incidence matrix of a symmetric block des ign. We present a new, elementary proof of Ryser's theorem and give a characterization of the incidence matrices of symmetric brock designs that involves eigenvalues of AAT. (C) Elsevier Science Inc., 1997.