Introduction to Linear Algebra, Fifth Edition: Gilbert Strang: 9780980232776: Amazon.com: Books

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Reviewed by Douglas Farenick, University of Regina Undergraduate mathematics textbooks are not what they used to be, and Gilbert Strang's superb new edition of Introduction to Linear Algebra is an example of everything that a modern textbook could possibly be, and more. First, let us consider the book itself. As with his classic Linear Algebra and its Applications (Academic Press) from forty years ago, Strang's new edition of Introduction to Linear Algebra keeps one eye on the theory, the other on applications, and has thestated goal of "opening linear algebra to the world" (Preface, page x).Aimed at the serious undergraduate student - though not just thoseundergraduates who fill the lecture halls of MIT, Strang's homeinstitution - the writing is engaging and personal, and the presentation is exceptionally clear and informative (even seasoned instructors maybenefit from Strang's insights). The first six chapters offer atraditional first course that covers vector algebra and geometry,systems of linear equations, vector spaces and subspaces, orthogonality, determinants, and eigenvalues and eigenvectors. The next three chapters are devoted to the singular value decomposition, lineartransformations, and complex numbers and complex matrices, followed bychapters that address a wide range of contemporary applications andcomputational issues. The book concludes with a brief but cogenttreatment of linear statistical analysis. I would like to stress that there is arichness to the material that goes beyond most texts at this level.Included are guides to websites and to OpenCourseWare, which I shallcomment upon later in this review.