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Max-algebra and pairwise comparison matrices, II

✍ Scribed by L. Elsner; P. van den Driessche

Publisher: Elsevier Science
Year: 2010
Tongue: English
Weight: 161 KB
Volume: 432
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2009.10.005

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✦ Synopsis

This paper is a continuation of our 2004 paper "Max-algebra and pairwise comparison matrices", in which the max-eigenvector of a symmetrically reciprocal matrix was used to approximate such a matrix by a transitive matrix. This approximation was based on minimizing the maximal relative error. In a later paper by Dahl a different error measure was used and led to a slightly different approximating transitive matrix. Here some geometric properties of this approximation problem are discussed. These lead, among other results, to a new characterization of a max-eigenvector of an irreducible nonnegative matrix. The case of Toeplitz matrices is discussed in detail, and an application to music theory that uses Toeplitz symmetrically reciprocal matrices is given.

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