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Following the Perron-Frobenius theorem, the spectral radius of a primitivematrix 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. Aniterative algorithm is presented to obtain matrix $B$ without an explicitknowledge of $X$. The convergence rate of this algorithm is similar to that ofthe power method but it uses less computational load. A byproduct of theproposed algorithm is a new method for calculating the first eigenvector.

A method for computing the Perron root for primitive matrices