Recommended Linear Algebra Texts

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Comments on:
Johnson, Riess, and Arnold, Introduction to Linear Algebra, 3rd ed., Addison-Wesley (1993).

I have used Johnson, Riess, and Arnold a couple of times and found it quite good. My colleagues here use it as well, and it seems to be a popular text among other technophiles. At first glance, you might think it is too elementary, but that's a misleading first impression. It has a good number of challenging exercises, and the mathematics is solid. The authors avoid the pitfall of a too-trivial first chapter and suddenly much more difficult theory chapter by introducing and using linear independence in the first chapter (on linear systems and matrix algebra). Chapter 2, on the basic theory, sticks to subspaces of R^n, but that does not turn out to be too simplistic for our students by any means. Then they treat abstact vector spaces in Chapter 4. So the effect is that the level of difficulty and abstraction increases more gradually than in most texts, and students get to revisit the most challenging topics. That aspect worked especially well.

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