ABSTRACT
The methods of linear algebra are most often used to solve sets of simultaneous linear equations. This chapter examines how matrix algebra can be used to describe the simultaneous linear equation problem. Matrix algebra ties the concept of a system to the idea of vector spaces. Vector spaces give a geometrical insight into the operation of systems. Simultaneous linear equations arise naturally in several radiologic applications. For example, when a gamma scintillation well counter is used to measure the radioactivity of two separate isotopes, and two energy windows are used. Some of the operations which can be performed on matrices are defined in an intuitive way. For example, matrix addition is adding the components of the two matrices. Image processing systems often have image processing operations. Images are two-dimensional arrays of numbers like matrices. The image addition operation is identical to the matrix addition operation.
