Modeling with Linear Algebra

This chapter aims to introduce the student to a variety of applications related to topics in linear algebra, including systems of linear equations, eigenvalues and eigenvectors, rowspace and nullspace. It reviews the concept of Markov chains, and introduces the student to real world applications related to discrete stochastic processes and the idea of model sensitivity to parameters in relation to linear models. The chapter explains the student to the terminology related to constraint based optimization and explores different techniques for solving constraint based optimization problems. It also introduces the student to the concept of singular value decomposition and how it can be used in modeling. The chapter also explores a variety of applications of linear regression and describes the student to basic concepts of error analysis. It examines the student to basic cost functions used with ordering functions.