The Schur Complement and the Number of Focal Points of a Symplectic Difference System

Abstract

We present new results connecting the number of focal points of a conjoined basis of а 2n × 2n symplectic difference system and the negative inertia index of the Schur complement in a symmetric matrix of the same size. The proved result makes it possible to reduce the problem of calculating of focal points for discrete symplectic systems to a saddle point spectral problem for a symmetric indefinite block matrix.