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On Bounded Matrices with Non-Negative Elements

Published online by Cambridge University Press:  20 November 2018

C. R. Putnam
C. R. Putnam*
Affiliation:
Purdue University
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It is known (Perron (10); Frobenius (5, 6)) that if A = (aik) is a finite matrix with elements aik ⩾ 0, then A has a real, nonnegative eigenvalue μ, satisfying μ =max|λ| where λ is in the spectrum of A, with a corresponding eigenvector x = (x1, … , xn) for which xi≥ 0. Moreover if aik > 0, then μ is a simple point of the spectrum with an eigenvector x (unique, except for constant multiples) with components xi ≥0. Much has been written on this and related issues; cf., for example, the recent papers (4, 12) wherein are given several references.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 10 , 1958 , pp. 587 - 591
Copyright
Copyright © Canadian Mathematical Society 1958

References

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