ABSTRACT
This chapter provides the essential background in matrix algebra. In order to proceed much further with the study of factor analysis, it is necessary to have some knowledge of matrix algebra, linear computation procedures, and a few results from m-dimensional Euclidean geometry. The elements of this matrix algebra are the same as the elements of ordinary algebra, namely the real numbers. In the expanded form, a matrix is written as a rectangular array, enclosed by brackets, by double vertical lines, or by parentheses or braces. The corresponding small letter with appropriate subscripts represents an element of this matrix written in the expanded form. In contrast to matrix addition and subtraction, the definition of matrix multiplication leads to several rules that do not parallel the rules of ordinary algebra. It is precisely this definition, however, which gives matrix algebra its considerable power in handling simultaneous linear equations, linear transformations, and the relations of m-dimensional Euclidean geometry.
