Lesson plan
Quadratic eigenvalue problem
In mathematics, the quadratic eigenvalue problem (QEP), is to find scalar eigenvalues \lambda , left eigenvectors y and right eigenvectors x such that : Q(\lambda)x = 0 ~ \text{ and } ~ y^\ast Q(\lambda) = 0, where Q(\lambda)=\lambda^2 M + \lambda C + K , with matrix coefficients M, \, C, K \in \mathbb{C}^{n \times n} and we require that M\,\neq 0 , (so that we have a nonzero leading coefficient). There are 2n eigenvalues that may be infinite or finite, and possibly zero. This is a special case of a nonlinear eigenproblem. Q(\lambda) is also known as a quadratic polynomial matrix.
Article summary
In mathematics, the quadratic eigenvalue problem (QEP), is to find scalar eigenvalues \lambda , left eigenvectors y and right eigenvectors x such that : Q(\lambda)x = 0 ~ \text{ and } ~ y^\ast Q(\lambda) = 0, where Q(\lambda)=\lambda^2 M + \lambda C + K , with matrix coefficients M, \, C, K \in \mathbb{C}^{n \times n} and we require that M\,\neq 0 , (so that we have a nonzero leading coefficient). There are 2n eigenvalues that may be infinite or finite, and possibly zero. This is a special case of a nonlinear eigenproblem. Q(\lambda) is also known as a quadratic polynomial matrix.
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Discussion questions
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