Basic matrix algebra: Manipulating vectors

Abstract

Statistics is, of course, a branch of applied mathematics. Consequently, anyone who wishes to understand statistics must first understand basic mathematics. In the case of simple regression analysis, we only need to be familiar with ordinary algebra. However, if we wish to understand multiple regression analysis, we must be familiar with the basic conventions and operations of matrix algebra. Statisticians routinely employ matrix algebra to describe multivariate models such as multiple regression analysis because it enables them to manipulate large systems of equations using compact algebraic expressions. Matrices consist of arrays of numbers or elements arranged in rows and columns. We can begin to understand matrix algebra by learning to manipulate the simplest matrices of all: vectors. A vector is an array consisting of a single row or column of numbers or elements.