Eigenvalues and Eigenvectors

Jonathan S. Golan ()
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Jonathan S. Golan: University of Haifa, Dept. of Mathematics

Chapter 12 in The Linear Algebra a Beginning Graduate Student Ought to Know, 2012, pp 255-296 from Springer

Abstract: Abstract Eigenvalues and the associated eigenvectors of an endomorphism of a vector space are defined and studied, as is the spectrum of an endomorphism. The characteristic polynomial of a matrix is considered and used to define the characteristic polynomial of the endomorphism of a finitely-generated vector space. This leads to the notions of geometric and algebraic multiplicities of eigenvalues. The minimal polynomial is then defined and studied. Among the theorems proven are the Cayley–Hamilton theorem and Burnside’s theorem. Von Mises’ algorithm for the computation of the dominant eigenvalue is introduced as an example of a iterative algorithm for eigenvalue computation.

Keywords: Vector Space; Characteristic Polynomial; Vector Space Versus; Minimal Polynomial; Distinct Eigenvalue (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-94-007-2636-9_12

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