  Following the Perron-Frobenius theorem, the spectral radius of a primitive
matrix is a simple eigenvalue. It is shown that for a primitive matrix $A$,
there is a positive rank one matrix $X$ such that $B = A \circ X$, where
$\circ$ denotes the Hadamard product of matrices, and such that the row
(column) sums of matrix $B$ are the same and equal to the Perron root. An
iterative algorithm is presented to obtain matrix $B$ without an explicit
knowledge of $X$. The convergence rate of this algorithm is similar to that of
the power method but it uses less computational load. A byproduct of the
proposed algorithm is a new method for calculating the first eigenvector.
