Non-linear spectra of matrices and extremal problems

Abstract

Theoretical questions and the computational aspects of the search for the spectral values λ and vectors xϵR^m{ϵ0} of a system A^τ(Ax)_(q) = λ^q(x)_(p), where A is a k × m matrix, 1 ⩽ p, q < ∞ are presented. When p = q = 2 this is simply the problem of determining the singular values of A. Nonlinear systems ((p − 2)² + (q − 2)² ≠ 0) arise in many fields of analysis, mechanics and approximation theory.