ABSTRACT
Matrices are down-to-earth computational devices consisting of rectangular arrays of numbers. This chapter focuses on square matrices which have the same number of rows as columns. Symmetries can be described in terms of them, and number rings can be constructed from them. The chapter discusses symmetries and coordinates in a square matrix. Two matrices are equal if they have the same numbers in the same places. The dimensions of a matrix are the number of rows (horizontal) and the number of columns (vertical). The chapter describes a two-by-two matrix having two rows and two columns by using examples. The complex numbers can be represented in a natural way by two-by-two matrices with entries in the real numbers. The chapter also discusses the construction of the quaternions as an algebraic analogue of the construction of non-Euclidean geometries.
