 
Summary: Normalized Prepared Bases for Discrete Symplectic
Matrix Systems
Douglas Anderson
Department of Mathematics and Computer Science, Concordia College
Moorhead, Minnesota 56562
andersod@cord.edu
Abstract
We will find conditions on one pair of a normalized prepared basis of a discrete sym
plectic matrix system that lead to the other pair being a dominant solution at . The
characterization of a recessive solution of the symplectic system at will also be given.
Key words: discrete symplectic matrix system, prepared solution, prepared basis, dominant and
recessive solutions
AMS Subject Classification: 39A10.
1 Introduction
Consider the discrete symplectic matrix system
Y (t + 1) = E(t)Y (t) + F(t)Z(t)
Z(t + 1) = G(t)Y (t) + H(t)Z(t)
(1)
on the discrete interval [a, ), where all matrices are n × n, and the coefficient matrix
E(t) F(t)
