STRUCTURE OF ALGEBRAS OF COMMUTATIVE MATRICES

Commutative spaces of matrices A = Sigma(k=1)(n) alpha(k)J(k) are stud ied, where {J(k)} is a set of (0, 1) matrices with prescribed sum S, a nd the alpha(k)'s are complex parameters. The great number of commutat ive spaces A obeying simple prescriptions on the first two rows of S c an all be described in terms of two basic algebras of matrices denoted by T-n and Gamma(n). A relationship between the structure of spaces A and the multiplicative complexity of the bilinear forms defined by th e J(k)'s is discussed.