A Note on Primitive Matrices
1954; Taylor & Francis; Volume: 61; Issue: 1 Linguagem: Inglês
10.1080/00029890.1954.11988404
ISSN1930-0972
Autores Tópico(s)Advanced Mathematical Theories and Applications
ResumoAbstract : Suppose that A is a square matrix consisting of nonnegative elements. In certain considerations it is important to know when all the elements of some power of A are strictly positive. Frobenius gave a very simple necessary and sufficient condition for this to happen. In this paper a simple proof of this result is given. This proof is algebraic in nature and avoids the use of the convergence of powers of a matrix.
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