Editing Perron–Frobenius theorem (section)

===Stochastic matrices===
A row (column) [[stochastic matrix]] is a square matrix each of whose rows (columns) consists of non-negative real numbers whose sum is unity. The theorem cannot be applied directly to such matrices because they need not be irreducible.

If ''A'' is row-stochastic then the column vector with each entry 1 is an eigenvector corresponding to the eigenvalue 1, which is also ρ(''A'') by the remark above. It might not be the only eigenvalue on the unit circle: and the associated eigenspace can be multi-dimensional. If ''A'' is row-stochastic and irreducible then the Perron projection is also row-stochastic and all its rows are equal.