The eigenproblem in max algebra
Date
2009-10-02T18:17:13Z
Authors
Bapat, R. B.
Stanford, David P.
van den Driessche, P.
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Abstract
The max algebra consists of the set of real numbers, along with negative infinity, equipped with two binary operations, maximization and addition. This algebra is useful in describing certain conventionally nonlinear systems in a linear fashion. Eigenvalues and eigenvectors of matrices over the max algebra are investigation, and proofs are presented for new results as well as for some known results not readily available in the literature. Properties of eigenvalues and eigenvectors that depend solely on the pattern of finite and infinite entries in the matrix are studied. Inequalities for the maximal eigenvalue of a matrix, motivated by those for the Perron root of a nonnegative matrix, are proved.
Description
Keywords
max-algebra, eigenvalue, eigenvector, circuit mean, Frobenius Normal Form