NON-NEGATIVE SQUARE MATRICES

Abstract

Non-negative indecomposable matrices are studied from the point of view of the Brouwer fixed point theorem; a concise proof of their basic properties is thus obtained. Properties of a general non-negative square matrix A are derived from those of non-negative indecomposable matrices. Theorems about the matrix sI-A are proved; they cover in a unified manner a number of results recurringly used in economics. A systematic study of the convergence of A(P) when p tends to infinity (A is a general complex matrix) is linked to combinatorial properties of non-negative square matrices.

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Document Details

Document Type
Technical Report
Publication Date
Aug 11, 1952
Accession Number
AD0604139

Entities

People

  • Gerard Debrue
  • I. N. Herstein

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Convergence
  • Economics
  • Eigenvectors
  • Equations
  • Hard Copy
  • Input Output Models
  • Permutations
  • Point Theorem
  • Rotation
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Theoretical Analysis.