Generalized Hermitian Eigenproblems
  J. Demmel

We assume that $A$ and $B$ are $n$ by $n$ Hermitian matrices and that $B$ is positive definite. We call $A - \lambda B$ a definite matrix pencil, or definite pencil for short. Here $\lambda$ is a variable rather than a constant.For convenience we will refer to eigenvalues, eigenvectors, and other properties of the pencil $A - \lambda B$.