Sterling M.J. Linear Algebra For Dummies

John Wiley & Sons, 2009. — 384 p.Linear algebra includes several different topics that can be investigated without really needing to spend time on the others. You really don’t have to read this book from front to back (or even back to front! ). You may be really, really interested in determinants and get a kick out of going through the chapters discussing them first. If you need a little help as you’re reading the explanation on determinants, then I do refer you to the other places in the book where you find the information you may need. In fact, throughout this book, I send you scurrying to find more information on topics in other places. The layout of the book is logical and follows a plan, but my plan doesn’t have to be your plan. Set your own route.The subject of linear algebra involves equations, matrices, and vectors, but you can’t really separate them too much. Even though a particular section focuses on one or the other of the concepts, you find the other topics working their way in and getting included in the discussion.Part I: Lining Up the Basics of Linear Algebra
In this part, you find several different approaches to organizing numbers and equations. The chapters on vectors and matrices show you rows and columns of numbers, all neatly arranged in an orderly fashion. You perform operations on the arranged numbers, sometimes with rather surprising results. The matrix structure allows for the many computations in linear algebra to be done more efficiently. Another basic topic is systems of equations. You find out how they’re classified, and you see how to solve the equations algebraically or with matrices.Part II: Relating Vectors and Linear Transformations
Part II is where you begin to see another dimension in the world of mathematics. You take nice, reasonable vectors and matrices and link them together with linear combinations. And, as if that weren’t enough, you look at solutions of the vector equations and test for homogeneous systems. Don’t get intimidated by all these big, impressive words and phrases I’m tossing around. I’m just giving you a hint as to what more you can do — some really interesting stuff, in fact.Part III: Evaluating Determinants
A determinant is a function. You apply this function to a square matrix, and out pops the answer: a single number. The chapters in this part cover how to perform the determinant function on different sizes of matrices, how to change the matrices for more convenient computations, and what some of the applications of determinants are.Part IV: Involving Vector Spaces
The chapters in this part get into the nitty-gritty details of vector spaces and their subspaces. You see how linear independence fits in with vector spaces. And, to top it all off, I tell you about eigenvalues and eigenvectors and how they interact with specific matrices.Part V: The Part of Tens
The last three chapters are lists of ten items — with a few intriguing details for each item in the list. First, I list for you some of the many applications of matrices — some things that matrices are actually used for in the real world. The second chapter in this part deals with using your graphing calculator to work with matrices. Finally, I show you ten of the more commonly used Greek letters and what they stand for in mathematics and other sciences.