ABSTRACT
Matrix algebra simply goes beyond the mere tabular display of data and deals with the algebraic manipulation of matrices. A matrix is a rectangular array of numbers arranged in several rows and columns. There are five important matrix operations: addition, subtraction, scalar multiplication, matrix multiplication, and matrix inversion. The first three matrix operations are basically defined on an element-by-element basis, whereas the last two are a little more complicated. The operation of matrix division is also very important in multivariate statistics. Most multivariate statistical techniques rely on determining the values of the characteristic roots of a matrix and their corresponding vectors. Although the computations of eigenvalues and eigenvectors are best left to computers, it is important that one understand the terms because they are used so frequently in multivariate statistics and because the properties of eigenvalues and eigenvectors can help in the characterization and assessment of a multivariate data analysis. This is basically the principle of the CayleyHamilton Theorem.
