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Primitivity of products of Leslie matrices

โœ Scribed by G.C. Taylor

Book ID
104272544
Publisher
Springer
Year
1985
Tongue
English
Weight
709 KB
Volume
47
Category
Article
ISSN
1522-9602

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โœฆ Synopsis

An earlier paper by E. L. Keller, 1980, Bull. marh. Biol. 42, 181-189, gave necessary and sufficient conditions for primitivity of a product of two Leslie matrices. This paper generalizes 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 does not retain its simplicity when generalized to higher order products.

๐Ÿ“œ SIMILAR VOLUMES

Primitivity of Permutation Groups, Coher
Primitivity of Permutation Groups, Coherent Algebras and Matrices
โœ Gareth A. Jones; Mikhail Klin; Yossi Moshe ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 114 KB

A coherent algebra is F-primitive if each of its non-identity basis matrices is primitive in the sense of Frobenius. We investigate the relationship between the primitivity of a permutation group, the primitivity of its centralizer algebra, and F-primitivity. The results obtained are applied to give