Generalized Inverses and Solutions to Systems of Linear Equations

Dale L. Zimmerman
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Dale L. Zimmerman: University of Iowa, Department of Statistics and Actuarial Science

Chapter 3 in Linear Model Theory, 2020, pp 43-56 from Springer

Abstract: 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 System of linear equations of the general form A x = b . $$\displaystyle \mathbf {A}\mathbf {x}=\mathbf {b}. $$ Here A is a specified n × m matrix called the coefficient matrix System of linear equations coefficient matrix of , b is a specified n-vector called the right-hand side vector System of linear equations right-hand side vector of , and x is an m-vector of unknowns. Any vector of unknowns that satisfies the system is called a solution System of linear equations solution to . A solution may or may not exist.

Date: 2020
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DOI: 10.1007/978-3-030-52063-2_3

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