The real linear eigenvalue problem in \(\mathbb C^n\)
A real linear operator \({\mathcal M}\) acts on \(\mathcal{C}^n\) according to \(z\rightarrow {\mathcal M}z=Mz+M_{\#}\bar{z}\) for a pair of matrices \(M,M_{\#} \in \mathcal{C}^{n\times n}\) called the linear and antilinear parts of \({\mathcal M}.\) If \({\mathcal M}_{\#}=0\) (resp. \({\mathcal M}=0\)) then \({\mathcal M}\) is called \(\mathcal{C}\)-linear (resp. antilinear). The spectrum of \({\mathcal M}\) consists of those points \(\lambda \in \mathcal{C}\) for which \(\lambda I-{\mathcal M}\) is not invertible giving rise to a bounded, possibly empty, real algebraic plane curve of degree \(2n.\) The authors presents results concerning the location of the eigenvalues of \({\mathcal M}\) and classify components of the spectrum. Path continuation techniques are implemented for computing components and subsets of the spectrum once an eigenvalue is available. Three numerical examples illustrating the aspect studied have been presented.
scientific article; zbMATH DE number 2137778
scientific article