Quadratic eigenvalue problem

In mathematics, the quadratic eigenvalue problem (QEP), is to find scalar eigenvalues λ {\displaystyle \lambda } , left eigenvectors y {\displaystyle y} and right eigenvectors x {\displaystyle x} such that Q ( λ ) x = 0 and y ∗ Q ( λ ) = 0 , {\displaystyle Q(\lambda )x=0~{\text{ and }}~y^{\ast }Q(\lambda )=0,} where Q ( λ ) = λ 2 M + λ C + K {\displaystyle Q(\lambda )=\lambda ^{2}M+\lambda C+K} , with matrix coefficients M , C , K ∈ C n × n {\displaystyle M,\,C,K\in \mathbb {C} ^{n\times n}} and we require that M ≠ 0 {\displaystyle M\,\neq 0} , (so that we have a nonzero leading coefficient). There are 2 n {\displaystyle 2n} eigenvalues that may be infinite or finite, and possibly zero.

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Quadratic eigenvalue problem

In mathematics, the quadratic eigenvalue problem (QEP), is to find scalar eigenvalues λ {\displaystyle \lambda } , left eigenvectors y {\displaystyle y} and right eigenvectors x {\displaystyle x} such that Q ( λ ) x = 0 and y ∗ Q ( λ ) = 0 , {\displaystyle Q(\lambda )x=0~{\text{ and }}~y^{\ast }Q(\lambda )=0,} where Q ( λ ) = λ 2 M + λ C + K {\displaystyle Q(\lambda )=\lambda ^{2}M+\lambda C+K} , with matrix coefficients M , C , K ∈ C n × n {\displaystyle M,\,C,K\in \mathbb {C} ^{n\times n}} and we require that M ≠ 0 {\displaystyle M\,\neq 0} , (so that we have a nonzero leading coefficient). There are 2 n {\displaystyle 2n} eigenvalues that may be infinite or finite, and possibly zero.

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Source: Wikipedia "Quadratic eigenvalue problem" · CC BY-SA 4.0

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