The algebraic structure of the set of square positive matrices is that of a semi-ring. The concept of a prime in the positive matrices has been introduced. A few examples of primes in the positive matrices are known but there is no general classification. In this paper a partial classification of primes in the positive matrices and in the doubly stochastic matrices is presented. The classification of primes in the doubly stochastic matrices is reduced to the classification of solutions to an index equation and a linear equation over a latin square.

Positive matrices and their generalizations; cones of matrices (msc 15B48), Factorization of matrices (msc 15A23), Stochastic matrices (msc 15B51)
CWI
Department of Operations Research, Statistics, and System Theory [BS]
System and control theory

Picci, G, van den Hof, J.M, & van Schuppen, J.H. (1995). A partial classification of primes in the positive matrices and in the doubly stochastic matrices. Department of Operations Research, Statistics, and System Theory [BS]. CWI.