Eigenvalue-eigenvector structure of Schoenmakers–Coffey matrices via Toeplitz technology and applications

The paper is concerned with the spectral properties of Green matrices and of a special subclass of the latter, known as Schoenmakers–Coffey matrices, which have a role in financial applications. The main results are related to the eigenvalue distribution of sequences of Green matrices of increasing size, while for the subclass of interest mentioned above, we also study the eigenvector oscillation structure: interestingly enough, even if these matrices are not shift invariant (Toeplitz), the results are obtained by using tools coming from Toeplitz technology. Indeed, for the asymptotic spectral distribution analysis, we use the theory of Generalized Locally Toeplitz sequences, while techniques taken from the study of Kac–Murdoch–Szegö matrices (again connected to Toeplitz matrices) are employed for the eigenvector oscillation structure results of the Schoenmakers–Coffey matrices. Few numerical tests are reported in order to illustrate the theoretical findings.