Abstract
Coherent algebras are defined to be the subalgebras of the matrix algebras M n ( C ) closed under Hadamard ( = coefficientwise) multiplication and containing the all 1 matrix, and are shown to be precisely the adjacency algebras of coherent configurations. Each such algebra has a type, which is a symmetric matrix with positive integer entries. The theory is illustrated by applications to quasisymmetric designs, which are essentially equivalent to coherent algebras of type 2 2 2 3 .
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