Quadratic eigenvalue problem: Difference between revisions

Revision as of 01:24, 16 September 2009

Revision as of 15:43, 28 March 2010

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:<math> Q(\lambda)x = 0\text{ and }y^\ast Q(\lambda) = 0,\, </math>

where <math>Q(\lambda)=\lambda^2 A_2 + \lambda A_1 + A_0\,</math>, with matrix coefficients <math>A_2, \, A_1, A_0 \in \mathbb{C}^{n \times n}</math> and <math>A_0\, \in \mathbb{C}^{n \times n}</math> and we require that <math>A_2\,\neq 0</math>, (so that we have a nonzero leading coefficient). There are <math>2n\,</math> eigenvalues that may be ''infinite'' or finite, and possibly zero. This is a special case of a [[nonlinear eigenproblem]]. <math>Q(\lambda)</math> is also known as a quadratic matrix polynomial.

==Applications==