Appendix B: A Matrix Refresher

Any student of linear algebra will welcome this textbook, which provides a thorough treatment of this key topic. Blending practice and theory, the book enables the reader to learn and comprehend the standard methods, with an emphasis on understanding how they actually work. At every stage, the authors are careful to ensure that the discussion is no more complicated or abstract than it needs to be, and focuses on the most fundamental topics.

W e will cover the basics of matrix algebra here. We will (i) describe what a matrix is, and then discuss (ii) matrix addition, (iii) matrix multiplication by a constant, (iv) multiplication of matrices, (v) the identity matrix, (vi) the inverse of a matrix, (vii) an algorithm for finding the inverse of a matrix, and (viii) the transpose of a matrix. We will then use matrix algebra to (ix) solve the simple problem of fitting a straight line between two points, and (x) the slightly more complex problem of fitting a straight line to three points. Finally, we will discuss (xi) eigenvectors and eigenvalues, including (xii) an algorithm to find them. While on the topic of matrix algebra we will describe three Excel commands you should probably know if you are going to manipulate matrices, and show a nice trick for exporting data from Excel into MATLAB. Excel and MATLAB are powerful tools for manipulating numerical data. To test your understanding of matrix algebra, a few problems (with solutions) are then presented.

Linear Algebra and its Applications, 1992

This two volume set of texts is designed to provide material for a course of up to one full year at the undergraduate level. It requires as a prerequisite some knowledge of calculus and complex numbers, but little mathematical

Some basic ideas from linear algebra play an essential role in our subject, so I'm o¤ering this summary as a reference. These notes won't substitute for a proper textbook. In particular, I won't give proofs of anything here. Nevertheless, I hope they will be of some use. I may add to these notes later the semester. (I won't add to them earlier).

A binary operation φ on a set A is a function from A × A to A, i.e., φ : A × A → A. φ((x, y)) is also denoted by xφy. Often we use a symbol for φ: +, ·, − , .