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# PEP_HYPERBOLIC

A quadratic eigenvalue problem with hyperbolic structure.

## Note

This is reserved for the case of a quadratic eigenvalue problem \((K+\lambda C+\lambda^2M)x=0\) with Hermitian coefficient matrices, and in addition \(M\) is positive definite and \((x^*Cx)^2>4(x^*Mx)(x^*Kx)\) for all nonzero \(x\in\mathbb{C}^n\). All eigenvalues are real, and form two separate groups of \(n\) eigenvalues, each of them having linearly independent eigenvectors.

## See Also

PEP: Polynomial Eigenvalue Problems, `PEPProblemType`, `PEPSetProblemType()`, `PEP_GENERAL`, `PEP_HERMITIAN`, `PEP_GYROSCOPIC`

## Level

intermediate

## Location

include/slepcpep.h

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