PUB - Publikationen an der Universität Bielefeld

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. (C) 2009 Elsevier Inc. All rights reserved.