Bounds for the Perron root of nonnegative matrices and spectral radius of iteration matrices

New bounds for the Perron root ρ(A) of a nonnegative matrix A are proposed. We prove thatmin1≤i≤n⁡ri(AB)ri(B)≤ρ(A)≤max1≤i≤n⁡ri(AB)ri(B) where B is an arbitrary matrix with row sums ri(B)=∑kbik>0, i=1,...,n. The bounds of H. Minc [1] and Shulin Liu [6] are both special cases of this result. And based on this result, we also get some bounds for the spectral radius of iteration matrices.