# Eigenvalue Problems

• J. Stoer
• R. Bulirsch
Part of the Texts in Applied Mathematics book series (TAM, volume 12)

## Abstract

Many practical problems in engineering and physics lead to eigenvalue problems. Typically, in all these problems, an overdetermined system of equations is given, say n + 1 equations for n unknowns ξ 1,..., ξ n of the form
$$F(x;\lambda ): \equiv \left[ {\begin{array}{*{20}{c}} {{f_1}({\xi _1}, \ldots ,{\xi _n};\lambda )} \\ { \ldots \ldots \ldots \ldots \ldots \ldots \ldots } \\ {{f_{n + 1}}({\xi _1}, \ldots ,{\xi _n};\lambda )} \end{array}} \right] = 0,$$
(6.0.1)
in which the functions f i also depend on an additional parameter λ. Usually, (6.0.1) has a solution x = [ξ 1,..., ξ n ] T only for specific values λ = λ i , i = 1, 2, ..., of this parameter. These values λ i are called eigenvalues of the eigenvalue problem (6.0.1), and a corresponding solution x = x(λ i ) of (6.0.1) eigensolution belonging to the eigenvalue λ i .

## Keywords

Eigenvalue Problem Characteristic Polynomial Minimal Polynomial Tridiagonal Matrix Elementary Divisor
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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