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Eigenvalue Problems

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Book cover Introduction to Scientific Computing and Data Analysis

Part of the book series: Texts in Computational Science and Engineering ((TCSE,volume 13))

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Abstract

The problem considered in this chapter is: given an n × n matrix A, find the number(s) \(\lambda\) and nonzero vectors x that satisfy

$$\displaystyle{ \mathbf{A}\mathbf{x} =\lambda \mathbf{x}. }$$
(4.1)

This is an eigenvalue problem, where \(\lambda\) is an eigenvalue and x is an eigenvector. There are a couple of observations worth making about this problem. First, x = 0 is always a solution of (4.1), and so what is of interest are the nonzero solutions. Second, if x is a solution, then α x, for any number α, is also a solution.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY, USA

    Mark H. Holmes

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  1. Mark H. Holmes
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Holmes, M.H. (2016). Eigenvalue Problems. In: Introduction to Scientific Computing and Data Analysis. Texts in Computational Science and Engineering, vol 13. Springer, Cham. https://doi.org/10.1007/978-3-319-30256-0_4

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