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Erschienen in:
2015 | OriginalPaper | Buchkapitel
15. Polynomials and the Fundamental Theorem of Algebra
verfasst von : Jörg Liesen, Volker Mehrmann
Erschienen in: Linear Algebra
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Abstract
In this chapter we discuss polynomials in more detail. We consider the division of polynomials and derive classical results from polynomial algebra, including the factorization into irreducible factors. We also prove the Fundamental Theorem of Algebra, which states that every non-constant polynomial over the complex numbers has a least one complex root. This implies that every complex matrix and every endomorphism on a (finite dimensional) complex vector space has at least one eigenvalue.