Editing Perron–Frobenius theorem (section)

==Terminology==
A problem that causes confusion is a lack of standardisation in the definitions. For example, some authors use the terms ''strictly positive'' and ''positive'' to mean > 0 and ≥ 0 respectively. In this article ''positive'' means > 0 and ''non-negative'' means ≥ 0. Another vexed area concerns ''decomposability'' and ''reducibility'': ''irreducible'' is an overloaded term. For avoidance of doubt a non-zero non-negative square matrix ''A'' such that 1&nbsp;+&nbsp;''A'' is primitive is sometimes said to be ''connected''. Then irreducible non-negative square matrices and connected matrices are synonymous.<ref>For surveys of results on irreducibility, see [[Olga Taussky-Todd]] and [[Richard A. Brualdi]].</ref>

The nonnegative eigenvector is often normalized so that the sum of its components is equal to unity; in this case, the eigenvector is the vector of a [[probability distribution]] and is sometimes called a ''stochastic eigenvector''.

''Perron–Frobenius eigenvalue'' and ''dominant eigenvalue'' are alternative names for the Perron root. Spectral projections are also known as ''spectral projectors'' and ''spectral idempotents''. The period is sometimes referred to as the ''index of imprimitivity'' or the ''order of cyclicity''.