Generalized Inverses and Solutions to Systems of Linear Equations

Abstract

Throughout this book we will discover that in order to obtain “good” estimators of the elements of β (or functions thereof) under a linear model, and for other purposes as well, we need to solve various systems of linear equations of the general form

$$\displaystyle \mathbf {A}\mathbf {x}=\mathbf {b}. $$

Here A is a specified n × m matrix called the coefficient matrix , b is a specified n-vector called the right-hand side vector , and x is an m-vector of unknowns. Any vector of unknowns that satisfies the system is called a solution . A solution may or may not exist.