The real linear eigenvalue problem in Cn

In this paper we study the real linear eigenvalue problem in Cn. We present results concerning the location of the eigenvalues of a real linear operator and classify components of the spectrum. Various families of real linear operators with structure are introduced for which the eigenvalue problem can be regarded, at least partially, as understood. We consider ways to achieve savings in computational complexity. Continuation techniques are implemented for locating components and subsets of the spectrum once an eigenvalue is available.