A NOTE ON PRIMITIVE MATRICES

Abstract

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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Document Details

Document Type
Technical Report
Publication Date
Nov 12, 1952
Accession Number
AD0604155

Entities

People

  • I. N. Herstein

Organizations

  • RAND Corporation

Tags

Communities of Interest

  • Energy and Power Technologies

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Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Mathematical Modeling and Probability Theory.