Exponents of classes of non-negative matrices

A square nonnegative matrix is said to be primitive if all the elements of some power of this matrix are positive. The least power that satisfies this condition is called the exponent of a primitive matrix. The least power such that all the matrices of the class to this power have only positive elements is called the exponent of the class of primitive matrices. We study bounds for the exponents of primitive matrices and classes of matrices.