Eigenvalues and Eigenvectors

Robert F. Brown

Chapter Chapter 18 in A Topological Introduction to Nonlinear Analysis, 2014, pp 125-135 from Springer

Abstract: Abstract This chapter describes a quite different sort of application of the fixed point index; it is an application to mathematics itself. For any function f : X → X $$f: X \rightarrow X$$ on a linear space, the definitions from linear algebra can be extended to call a real number λ an eigenvalue of f if f(x) = λ x for some x ≠ 0 in X, and then x is an eigenvector for the eigenvalue λ.

Keywords: Eigenvectors; Fixed Point Index; Normed Linear Space; Krein-Rutman Theorem; Compact Linear Operator (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-319-11794-2_18

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