1. Asymptotic formulae and inequalities for point spectrum in max algebra
- Author
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Aljoša Peperko, H. Shokooh Saljooghi, and Seyed Mahmoud Manjegani
- Subjects
Max algebra ,Numerical Analysis ,Pure mathematics ,Algebra and Number Theory ,Spectral mapping ,Hadamard transform ,Spectrum (functional analysis) ,Discrete Mathematics and Combinatorics ,Point (geometry) ,Geometry and Topology ,Geometric mean ,Eigenvalues and eigenvectors ,Mathematics - Abstract
We prove new explicit asymptotic formulae between (geometric) eigenvalues in max-algebra and classical distinguished eigenvalues of nonnegative matrices, which are useful tools for transferring results between both settings. We establish new inequalities for both types of eigenvalues of Hadamard products and Hadamard weighted geometric means of nonnegative matrices. Moreover, a version of the spectral mapping theorem for the distinguished spectrum is pointed out.
- Published
- 2022
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