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The Structure of Powers of Non-Negative Matrices

Published online by Cambridge University Press:  20 November 2018

A. L. Dulmage  and
N. S. Mendelsohn
A. L. Dulmage
Affiliation:
University of Alberta and University of Manitoba
N. S. Mendelsohn
Affiliation:
University of Alberta and University of Manitoba
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The theory of non-negative matrices was initiated by Perron (7) and Frobenius (4). Wielandt in (11) gives an elegant exposition of the subject.

It is well known to workers in the field that if a matrix A has all its entries non-negative real numbers, then the pattern of zeros and non-zeros of A completely determines the pattern of zeros and non-zeros in every power of A. Ptak in (8) and Ptak and Sedlacek in (9) describe this behaviour in terms of some combinatorial constructs.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 318 - 330
Copyright
Copyright © Canadian Mathematical Society 1965

References

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