Involutory Matrices Over Finite Commutative Rings.

An n x n matrix is called involutory if and only if A squared I sub n where I sub n is the n x n identity matrix. This paper is concerned with involutory matrices over an arbitrary finite commutative ring R with identity and with the similarity relation among such matrices. In particular the authors seek a canonical set C with respect to similarity for the n x n involutory matrices over R i.e., a set C of n x n involutory matrices over R with the property that each n x n involutory matrix over R is similar to exactly one matrix in C.