Pseudoprime factorizations of integer matrices

We give a method of factoring integer matrices in Zn×n into components such that the factorization is not unique unless certain information is known. In Section 2, we introduce this method of factorization and provide theorems which establish its well-definedness. In Section 3, we construct a matrix in SL(n,Z) as a product of specific types of matrices and establish an algorithm for factoring the result uniquely given an amount of information.