Abstract linear algebra
by Morton Landers Curtis · first published 1990
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Beginning from scratch and developing the standard topics of Linear Algebra, this book is intended as a text for a first course on the subject. The goal to which this work leads is the Theorem of Hurwitz - that the only normed algebras over the real numbers are the real numbers, the complex numbers, the quaternions, and the octonions. Unique in presenting this material at an elementary level, the book stresses the complete logical development of the subject and will provide a bavuable reference for mathematicians in general.
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Honestly, I'm not even sure how much a review would help either. I struggled quite a bit with linear algebra in school with Curtis' Abstract Linear Algebra, and eventually I decided to hole up in the math library for the better part of a week and went through every linear algebra book they had (definitely more than 33) to find the best supplementary material.…
on “The best linear algebra books” ↗…known as backward and forward errors -- depending on what you need. * * * Incidentally, this is the kind of stuff that's covered in Golub and Van Loan, or in Trefethen and Bao, but not in a standard Abstract Linear Algebra book. For instance, Strang's book spends only one chapter on numerical linear algebra.
on “Surprises from numerical linear algebra (2010)” ↗