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Nonlinear eigenvalue–eigenvector problems for STP matrices

Published online by Cambridge University Press:  12 July 2007

Uri Elias  and
Allan Pinkus
Uri Elias
Affiliation:
Department of Mathematics, Technion, IIT, Haifa 32000, Israel
Allan Pinkus
Affiliation:
Department of Mathematics, Technion, IIT, Haifa 32000, Israel
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Abstract

Let Ai, i = 1, …, m, be a set of Ni × Ni−1 strictly totally positive (STP) matrices, with N0 = Nm = N. For a vector x = (x1, …, xN) ∈ RN and arbitrary p > 0, set We consider the eigenvalue-eigenvector problem where p1 … pm−1 = r. We prove an analogue of the classical Gantmacher-Krein theorem for the eigenvalue-eigenvector structure of STP matrices in the case where pi ≥ 1 for each i, plus various extensions thereof.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 132 , Issue 6 , December 2002 , pp. 1307 - 1331
Copyright
Copyright © Royal Society of Edinburgh 2002

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