Appendix to chapter 2

Abstract

Appendix to Chapter 2 This appendix has two purposes. One is to reformulate the exemplar model using matrix algebra. This is important for speeding up the computational process, shortening the length of the code, and simplifying the program. Furthermore, matrix operators are quite useful for other topics covered in this book. The second purpose is to describe the computer program that was used to qualitatively analyze the predictions of the exemplar model (i.e., the program used to compute Figure 6.) Review of Matrix Algebra. Matrix algebra is a mathematical formalism that based on objects called column vectors, row vectors, and matrices; as well as matrix operators such as transpose, matrix sum, scalar multiplication, inner product, matrix product, and Kronecker product, and matrix inverse. For our purposes, an n by m matrix is just a table of values that has n rows and m columns, and the entire table is denoted by a bold face letter such as X. An example of a 2 (row) by 3 (column) matrix is shown below.