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ISBN: 9781304912794

This is a book on linear algebra and matrix theory. While it is self contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader has had calculus. Some optional topics require more analysis than this, however. I think that the subject of linear algebra is likely the most significant topic discussed in undergraduate mathematics courses. Part of the reason for this is its usefulness in unifying so many different topics. Linear algebra is essential in analysis, applied math, and even in theoretical mathematics. This is the point of view of this book, more than a presentation of linear algebra for its own sake. This is why there are numerous applications, some fairly unusual.

(CC BY) This is an introduction to linear algebra. The main part of the book features row operations and everything is done in terms of the row reduced echelon form and speciﬁc algorithms. At the end, the more abstract notions of vector spaces and linear transformations on vector spaces are presented. However, this is intended to be a ﬁrst course in linear algebra for students who are sophomores or juniors who have had a course in one variable calculus and a reasonable background in college algebra.