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The one thing I really enjoy about his texts is that his writing, even on basic material, sometimes contains very deep insights into the underlying structure of the mathematics. Understanding a Strang textbook is the difference between actually _understanding_ mathematics and just being able to do it.
So I heartily endorse this book. If you want a higher-level text, I'd suggest Demmel's Applied Numerical Linear Algebra. But reading this book still wouldn't hurt.
Sure, Strang's book may not be an adequate sole text from which to learn linear algebra and matrix theory. But surely serious mathematicians (as opposed to kindergarteners) would never attempt to learn a subject from a single text.
This is where the book shines - as a supplement to a more formal text. (Here, pick your own; I have my own personal favorite, but it has been out of press for years). And then read the two side by side. One provides rigor, the other, INTUITIVE UNDERSTANDING. This, after all, is where Strang's book shines - rather than providing only a formal understanding of the mathematics in question, he manages to convey an intuitive understanding of the objects represented by linear algebra methods in many common applications.
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