ABSTRACT
This chapter explores how the methods of linear algebra can be used to describe systems. The convolution model is the most common method of describing linear, time invariant systems. The linear algebra model relies on the fact that the system is linear, but does not require that it be time invariant. Because it does not impose the time invariant restriction on system it can be used to model a much wider class of systems. In the linear algebra model of systems, vectors are used to represent the input and the output signals, and matrices are used to represent systems. Discrete convolution is a method of describing linear, time invariant systems. The major advantage of linear algebra approach over the linear systems approach is that it can be used to describe systems which are not shift invariant. The linear algebra description of a system uses vectors, which are one dimensional, as input and output signals. Yet images are two-dimensional signals, images.
