A First Course in Linear Algebra is an introductory textbook designed for university sophomores and juniors. Typically such a student will have taken calculus, but this is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form. Along the way, determinants and eigenvalues get fair time.

1. Linear Algebra Courses Online

Linear Algebra Courses Online

There is a comprehensive and are available to download for printing or on-screen viewing. Physical copies may be purchased from the print-on-demand service. It seems therefore desirable to give permanent form to the lessons of experience so that others can benefit by them and be encouraged to undertake similar work. Cundy and A.P. Rollet, Mathematical Models, 1952 This textbook has more freedom than most (but see ).

First, there is no cost to acquire this text, and you are under no obligation whatsoever to compensate or donate to the author or publisher. So in this most basic sense, it is a free textbook. Therefore you can also make as many copies as you like, ensuring that the book will never go out-of-print. You may modify copies of the book for your own use - for example, you may wish to change to a prefered notation for certain objects or add a few new sections.

I have applied a copyright to the book, and subsequently licensed it with a (GFDL). It is this combination that allows me to give you greater freedoms in how you use the text, thus liberating it from some of the antiquated notions of copyright that apply to books in physical form. The main caveat is that if you make modifications and then distribute a modified version, you are required to again apply the GFDL license to the result so that others may benefit from your modifications.

If nature has made any one thing less susceptible than all others of exclusive property, it is the action of the thinking power called an idea, which an individual may exclusively possess as long as he keeps it to himself; but the moment it is divulged, it forces itself into the possession of every one, and the receiver cannot dispossess himself of it. Its peculiar character, too, is that no one possesses the less, because every other possesses the whole of it. Thomas Jefferson, to Isaac McPherson, August 13, 1813 It is hoped that by this arrangement, others will help improve the book through rapid correction of errors and contributions of exercises and new material. Examine an, and if you like what you see, consider a to support this experiment in providing quality textbooks at reasonable prices. 'Instructors who wish to teach a pure linear algebra course that emphasizes rigor and formal mathematics will be able to make good use of this material and feel secure in the knowledge that the book is not going to go out of print. Finally, the price is right.' SIAM Review, Book Reviews, December 2007.

Suitable for advanced undergraduates and graduate students, this text offers a complete introduction to the basic concepts of linear algebra. Interesting and inspiring in its approach, it imparts an understanding of the subject's logical structure as well as the ways in which linear algebra provides solutions to problems in many branches of mathematics. The authors define general vector spaces and linear mappings at the outset and base all subsequent developments on these concepts. This approach provides a ready-made context, motivation, and geometric interpretation for each new computational technique. Proofs and abstract problem-solving are introduced from the start, offering students an immediate opportunity to practice applying what they've learned. Each chapter contains an introduction, summary, and supplementary exercises.

The text concludes with a pair of helpful appendixes and solutions to selected exercises.