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Linear Algebra Done Right 2ND Editionby Sheldon Axler
Synopses & ReviewsPublisher Comments:This text for a second course in linear algebra is aimed at math majors and graduate students. The novel approach taken here banishes determinants to the end of the book and focuses on the central goal of linear algebra: 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 presentswithout having defined determinantsa clean proof that every linear operator on a finitedimensional complex vector space (or an odddimensional real vector space) has an eigenvalue. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. No prerequisites are assumed other than the usual demand for suitable mathematical maturity. Thus, the text starts by discussing vector spaces, linear independence, span, basis, and dimension. Students are introduced to innerproduct spaces in the first half of the book and shortly thereafter to the finitedimensional spectral theorem. This second edition includes a new section on orthogonal projections and minimization problems. The sections on selfadjoint operators, normal operators, and the spectral theorem have been rewritten. New examples and new exercises have been added, several proofs have been simplified, and hundreds of minor improvements have been made throughout the text.
Synopsis:This text for a second course in linear algebra is aimed at math majors and graduate students. The approach is novel, banishing determinants to the end of the book and focusing on the central goal of linear algebra: understanding the structure of linear operators on vector spaces.
Synopsis: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.
Table of Contents1: Vector Spaces 2: FiniteDimensional Vector Spaces 3: Linear Maps 4: Polynomials 5: Eigenvalues and Eigenvectors 6: InnerProduct Spaces 7: Operators on InnerProduct Spaces 8: Operators on Complex Vector Spaces 9: Operators on Real Vector Spaces 10: Trace and Determinant
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