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Undergraduate Texts in Mathematics
Linear algebra
This popular and successful text was originally written for a one-semester course in linear algebra at the sophomore undergraduate level. Students at this level generally have had little contact with complex numbers or abstract mathematics, so the book deals almost exclusively with real finite dimensional vector spaces, but in a setting and formulation that permits easy generalization to abstract vector spaces. The goal of the first two editions was the principal axis theorem for real symmetric linear transformation. The principal axis theorem becomes the first of two goals for this new edition, which follows a straight path to its solution. A wide selection of examples of vector spaces and linear transformation is presented to serve as a testing ground for the theory. In the second edition, a new chapter on Jordan normal form was added which reappears here in expanded form as the second goal of this new edition, along with applications to differential systems. To achieve the principal axis theorem in one semester a straight path to these two goals is followed. As compensation, there is a wide selection of examples and exercises. In addition, the author includes an introduction to invariant theory to show students that linear algebra alone is not capable of solving these canonical forms problems. The book continues to offer a compact, but mathematically clean introduction to linear algebra with particular emphasis on topics that are used in abstract algebra, the theory of differential equations, and group representation theory.
- GenresMathematics
280 pages, Hardcover
First published January 1, 1978
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May 13, 2014
This is a great introduction to linear algebra. I was reading it to review doing proofs...plus it's my habit to annually review linear algebra.
The exercises range from great to "Why is this here?" and sometimes "That's a sentence, not an exercise". They are not the "calculation" family of exercises, where one does a large number of matrix multiplications, determinants, finding the inverses, etc. This is a first step towards proof-based thinking.
But the proofs really are quite well done. The best exercise for the reader is to pause after a given proof, and ask one's self "IS there another way to do this? What if we remove some axioms? What if we work with a Rig instead of a field?" etc.
If the exercises were updated and/or revised, this would be a 5 star book. But since the exercises are a seeming after thought, I can't bring myself about to give it such a ranking...
The exercises range from great to "Why is this here?" and sometimes "That's a sentence, not an exercise". They are not the "calculation" family of exercises, where one does a large number of matrix multiplications, determinants, finding the inverses, etc. This is a first step towards proof-based thinking.
But the proofs really are quite well done. The best exercise for the reader is to pause after a given proof, and ask one's self "IS there another way to do this? What if we remove some axioms? What if we work with a Rig instead of a field?" etc.
If the exercises were updated and/or revised, this would be a 5 star book. But since the exercises are a seeming after thought, I can't bring myself about to give it such a ranking...
Displaying 1 of 1 review