"The aim of this small volume is to engage in applications of linear algebra. The focus is on motivation and raising interest rather than on teaching. It isn''t a textbook, so you will find no systematic theory and only very few proofs, but nevertheless it covers the foundations sufficiently to enable the reader to understand the offered applications and develop some of his own. Only very little previous knowledge is necessary to benefit from the book. The main content are real-life applications of linear algebra, and their list is impressive. Even the very concept of a matrix is introduced by image processing, then it goes on with ratings of movies, recognizing handwriting, clustering, ranking of web pages, face recognition and many more. Surely the reader will be surprised by them. The list of mathematical concepts used is also long: norms and scalar products, homogeneous coordinates, isometries, Gaussian elimination, linear regression, eighenvalues, Markov chains, principal component analysis and singular value decomposition, the latter playing a major role in many of the given applications.

As the volume serves more as an appetizer, nearly no references to textbooks on linear algebra are given, instead the list of literature provides links to the applications themselves, many up-to-date, and the author point to Google as a source for further information. So, if you can''t imagine what linear algebra is good for, read this book, get captivated, and start to explore on you own."" - Dieter Riebesehl, Zentrallblatt MATH ""One of the nice things about linear algebra, I''ve always thought, is that there is something in the subject for just about everybody. There''s a lot of beautiful theory, but at the same time those people who like to roll up their sleeves and get their hands dirty with computations, particularly in aid of interesting applications, will find much here to interest them as well. What the author has done in this slim (about 130 pages of text) book is to assemble a potpourri of interesting applications of linear algebra and discuss each one, if not exhaustively, in at least sufficient detail to give a reader a sense of how linear algebra enters the picture. The primary focus is on computer graphics and data mining, but the reader will also see discussions of cryptography, least squares approximation, compressed sensing, Markov processes and the Google page rank algorithm, fractals, and sports ranking ""bracketology."" In addition to discussing applications, Chartier also develops the linear algebra that is necessary to understand them, though not the kind of depth that one sees in a standard (four times as large) introductory text. This book is, therefore, not intended as a substitute for such texts; instead, linear algebra topics are introduced only to the extent that they are necessary to help explain some application.

So, for example, matrix multiplication is defined, but determinants are not (at least not for general square matrices; the 2x2 case is mentioned, however). The author''s development of this background linear algebra is quite concise and not accompanied by the myriad examples that we see in the usual textbooks on the subject. There are also no exercises. I therefore see this book as being most useful as an adjunct to an introductory course in linear algebra-either as an assigned supplementary text or as a desk reference for instructors wanting to spice up their own lectures with interesting examples that likely go beyond the coverage of the assigned text. Used in this way, I think it could be very valuable. The writing is clear, the applications are interesting, and a student with some knowledge of linear algebra would benefit greatly from knowing the material in this book."" - Mark Hunacek, MAA Reviews ""The level of difficulty is not high, a college course in linear algebra is not even necessary for understanding. All that is needed for background is an understanding of more complex linear systems, some trigonometry and the basic operations on matrices.

Segments could be pulled out to be as used as supplements for high school courses, college courses in finite mathematics and to answer the standard question, ""What will we ever use math for?"" The sections on computer graphics and March Madness are the ones that most readers will best relate to. Nearly all people are familiar with the power of computer graphics from watching movies and the number of NCAA basketball tournament office pools is enormous. Even someone that does not know matrix algebra should be able to understand the section on the relative ranking of teams. Math can be fun and it can be useful, a small percentage of people consider it both. With the existence of this book, that percentage will rise."" - Charles Ashbacher.