Abstract
An earlier paper by E. L. Keller, 1980,Bull. math. Biol. 42, 181–189, gave necessary and sufficient conditions for primitivity of a product of two Leslie matrices. This paper generalized that result to an arbitrary number of Leslie matrices. The generalized result shows that Keller's is, from one viewpoint, more conveniently stated in a slightly different form (our equation (6)). This restatement in turn simplifies the proof of his special case of the general result. It also shows that the case of products of just pairs of matrices is a special one in that the simple form of result obtained for that case doesnot retain its simplicity when generalized to higher order products.
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Literature
Keller, E. L. 1980. “Primitivity of the Product of Two Leslie Matrices.”Bull. math. Biol. 42, 181–189.
Rosenblatt, D. 1957. “On the Graphs and Asymptotic Forms of Finite Boolean Relation Matrices and Stochastic Matrices.”Nav. Res. Logist. Q. 4, 151–167.
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Taylor, G.C. Primitivity of products of leslie matrices. Bltn Mathcal Biology 47, 23–34 (1985). https://doi.org/10.1007/BF02459644
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DOI: https://doi.org/10.1007/BF02459644