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# ๐ Linear Algebra Done Right by Sheldon Axler โ free epub

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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 presents--without having defined determinants--a clean proof that every linear operator on a finite- dimensional complex vector space (or an odd-dimensional 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 inner-product spaces in the first half of the book and shortly thereafter to the finite-dimensional spectral theorem. This second edition includes a new section on orthogonal projections and minimization problems. The sections on self-adjoint 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. ## About book:

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FROM THE REVIEWS:

AMERICAN MATHEMATICAL MONTHLY "The determinant-free proofs are elegant and intuitive."

CHOICE "Every discipline of higher mathematics evinces the profound importance of linear algebra in some way, either for the power derived from its techniques or the inspiration offered by its concepts. Axler demotes determinants (usually quite a central technique in the finite dimensional setting, though marginal in infinite dimensions) to a minor role. To so consistently do without determinants constitutes a tour de forces in the service of simplicity and clarity; these are also well served by the general precision of Axler's prose. Students with a view towards applied mathematics, analysis, or operator theory will be well served. The most original linear algebra book to appear in years, it certainly belongs in every undergraduate library." ZENTRALBLATT MATH "Altogether, the text is a didactic masterpiece."

- Series:
**Undergraduate texts in mathematics** - Author:
**Sheldon Axler** - Year:
**1997** - Publisher:
**Springer** - Language:
**English** - ISBN:
**9780387982588,0387982582,0387982590**

- File size:
**3 779 905** - Format:
**pdf**

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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 lin...

This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: u...

Perhaps my love of this text is because I was one of those students who only wanted to know how to use a derivative or integral to solve a physical problem when I took my first calculus class in 1973. Years later when I was visiting MIT looking for econom...

An introduction to the calculus, with an excellent balance between theory and technique. Integration is treated before differentiation - this is a departure from most modern texts, but it is historically correct, and it is the best way to establish the tr...

An introduction to the calculus, with an excellent balance between theory and technique. Integration is treated before differentiation - this is a departure from most modern texts, but it is historically correct, and it is the best way to establish the tr...

Further Linear Algebra is a natural sequel to the authors' highly acclaimed SUMS volume "Basic Linear Algebra". The more advanced topics covered here take the reader to the very heart of the subject, and include inner product spaces, direct sums of subspa...

Evolving from an elementary discussion, this book develops the Euclidean algorithm to a very powerful tool to deal with general continued fractions, non-normal Padรฉ tables, look-ahead algorithms for Hankel and Toeplitz matrices, and for Krylov subspace me...