Accession Number:

AD0604155

Title:

A NOTE ON PRIMITIVE MATRICES

Descriptive Note:

Corporate Author:

RAND CORP SANTA MONICA CA

Personal Author(s):

• Herstein, I. N.

Report Date:

1952-11-12

Pagination or Media Count:

6.0

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.

Descriptors:

• *MATRICES(MATHEMATICS)
• ALGEBRA
• DETERMINANTS(MATHEMATICS)
• THEOREMS

Subject Categories:

• Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE