# Linear Algebra Done Right

Springer, Jul 18, 1997 - Mathematics - 251 pages
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.

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#### Review: Linear Algebra Done Right

User Review  - Jamie Banks - Goodreads

Wonderful!!!! No determinants til the end. Emphasis on concept over formal, so rare in Lin alg. Weak on determinants - Artin or Halmos, Finite Dimensional Vector Spaces, are better. The only reason I understand Graham-Schmidt conceptually and not as an algorithm to be memorized!!! Read full review

#### Review: Linear Algebra Done Right

User Review  - Joshua Goller - Goodreads

My go-to recommendation for linear algebra. Clear, concise, and helpful. An actual math book; not another "vectors are thingies with magnitude and direction herp derp" text for electrical engineers. Read full review