Structure of algebras of commutative matrices Original Research Article

Commutative spaces of matrices A = ∑nk=1 akJk are studied, where {Jk} is a set of (0, 1) matrices with prescribed sum S, and the akʹs are complex parameters. The great number of commutative spaces A obeying simple prescriptions on the first two rows of S can all be described in terms of two basic algebras of matrices denoted by Tn and Γn. A relationship between the structure of spaces A and the multiplicative complexity of the bilinear forms defined by the Jkʹs is discussed.