Eigenvalues and eigenvectors

Ian Jacques and Colin Judd
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Ian Jacques: Coventry Lanchester Polytechnic, Department of Mathematics
Colin Judd: Coventry Lanchester Polytechnic, Department of Mathematics

Chapter 4 in Numerical Analysis, 1987, pp 71-128 from Springer

Abstract: Abstract In this chapter we describe numerical techniques for the calculation of a scalar λ and non-zero vector x in the equation 4.1 $$ Ax = \lambda x $$ where A is a given n × n matrix. The quantities λ and x are usually referred to as an eigenvalue and an eigenvector of A. They arise in many different branches of mathematics including quadratic forms, differential systems and non-linear optimization, and can be used to solve problems from such diverse fields as economics, information theory, structural analysis, electronics and control theory.

Keywords: Tridiagonal Matrix; Dominant Eigenvalue; Inverse Iteration; Hessenberg Matrix; Hessenberg Form (search for similar items in EconPapers)
Date: 1987
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DOI: 10.1007/978-94-009-3157-2_4

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