Advanced Linear Algebra (Graduate Texts in Mathematics) Hardcover – Import, 9 November 2007

This is an excellent book for consolidating and expanding upon topics covered in the first few years of an undergraduate degree. It begins by revisiting material from introductory linear algebra, but does so in a much more mature "abstract algebra" setting which acts as a pleasant stepping stone into the more graduate-level style. There is a decent survey of module theory which is often neglected or missing from undergraduate texts and It also covers a lot of concepts which I had some vague notion of but hadn't found the right path to investigate; tensor products, graded algebras, exterior product and symplectic and affine geometries, to name a few. Much more than that I really can't speak highly enough of the author's pedagogical skill. He imparts information in a clear concise way, but in such a way that everything comes across as natural and obvious. Opening a section of the book at random may look daunting at first, but you won't have to read more than a few sentences before the ideas emerge in sharp relief and you genuinely feel like you've understood something significant. The best way I can describe it is it's as though he has explained something the way I would have explained it to myself had I already understood it. Maybe I just have a particular affinity with the style, but I suspect it is more universal than that. All in all I would highly recommend the text to anyone looking to recast their undergraduate material on a stronger footing, either in preparation for further study or even as a summer read before beginning their third or fourth year.

Very good book. Roughly equivalent to a version John Conway's book on Functional Analysis without the Topology or Analysis.

Excellent

This is the second edition of Steven Roman's text on linear algebra. The first edition was very good but the typesetting was somewhat amateurish. This edition corrects that problem beautifully and offers a much expanded range of topics. The material is well motivated, the proofs are detailed, and the writing is clear. It is ideal for self-study for somone with a background in introductory linear algebra who wishes to delve more deeply into advanced topics.So why only 3 stars? Answer: after minimal use the binding cracked, and it will only be a matter of time before pages start falling out. Springer should be ashamed at distributing such a poorly bound book. I've purchased a number of Springer books lately, and this is not the only time I've been disappointed at poor production quality. If I were Steve Roman, I would be upset that my otherwise excellent text is being sold with such an inferior binding (at least in my copy). If you purchase this book - and you should - check immediately that the binding is satisfactory.

The perfect bridge between linear algebra and module theory