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Rev., 43 (2001), pp. 235–286.</ref> (QEP)''', is to find [[scalar (mathematics)|scalar]] [[eigenvalue]]s <math>\lambda</math>, left [[eigenvector]]s <math>y</math> and right eigenvectors <math>x</math> such that
:<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 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 [[polynomial matrix]].
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