 
Summary: Discrete Trigonometric Matrix Functions
Douglas R. Anderson
Department of Mathematics and Computer Science, Concordia College
Moorhead, MN 56562
andersod@cord.edu
Abstract
We explore a pair of matrix solutions to a certain discrete system which has vari
ous properties similar to the familiar continuous trigonometric functions, including basic
identities and sum and difference of two angles formulas. Then we examine separation
properties of these matrices. An oscillation result is also given.
Key words: difference equations, discrete symplectic systems, generalized zeros.
AMS Subject Classification: 39A10.
In this paper we will define the discrete trigonometric matrix functions. The continuous
trigonometric matrix functions have been studied by Barrett [3], Etgen [5], and Reid [11]. We
will assume the reader has only had a first course in difference equations. Elementary books on
the subject include Elaydi [4], Jerri [7], Kelley and Peterson [8], and Mickens [10]. Some other
books in the area include Agarwal [1], Ahlbrandt and Peterson [2], and Lakshmikantham and
Trigiante [9].
Let Q(t) be an n × n Hermitian matrix function on the discrete interval [a, ) {a, a +
1, . . .}. We define the discrete sine and cosine matrix functions
