Abstract
The purpose of this introductory chapter is twofold. First, it supplies a unified discussion of the most important operator theoretic properties of positive square matrices; it can be read independently of the remainder of the book, presupposing only familiarity with elementary polynomial algebra (cf. § 1). Second, and more important in our context, this first chapter is intended to serve as a motivation for the study of positive operators on Banach lattices—the central theme of this book. As in the later chapters, the ideal structure of a vector lattice (cf. Chapter II, § 2) is used extensively and advantageously in Chapter I; even in the finite dimensional case discussed here, the judicious use of ideal theory turns out to be the key to many fruitful insights.
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© 1974 Springer-Verlag Berlin Heidelberg
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Schaefer, H.H. (1974). Positive Matrices. In: Banach Lattices and Positive Operators. Die Grundlehren der mathematischen Wissenschaften, vol 215. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-65970-6_1
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DOI: https://doi.org/10.1007/978-3-642-65970-6_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-65972-0
Online ISBN: 978-3-642-65970-6
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