Linear Algebra Done Right (Undergraduate Texts in Mathematics)
by Sheldon Axler
Paperback:  251 pages 
Publisher:  Springer (Feb 26, 2004) 
Language:  English

ISBN10:  0387982582 
ISBN13:  9780387982588 
This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents  without having defined determinants  a clean proof that every linear operator on a finitedimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to innerproduct spaces in the first half of the book and shortly thereafter to the finite dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on selfadjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text..
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