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On the eigenproblem of matrices over distributive lattices

✍ Scribed by Yijia Tan

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
158 KB
Volume
374
Category
Article
ISSN
0024-3795

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✦ Synopsis

Let (L, , ∨, ∧) be a complete and completely distributive lattice. A vector ξ is said to be an eigenvector of a square matrix A over the lattice L if Aξ = λξ for some λ in L. The elements λ are called the associated eigenvalues. In this paper, we obtain the maximum eigenvector of A for a given eigenvalue λ, and give some properties of the maximum matrix M(λ, ξ ) in T (λ, ξ), the set of matrices with a given eigenvector ξ and eigenvalue λ. We also consider the structure of matrices which possess a given primitive eigenvector ξ and show in particular that, for any given λ in L, there is a matrix, namely M(λ, ξ ), having ξ as a maximal primitive eigenvector associated with the eigenvalue λ.

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