Linear Algebra / Edition 3

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This book begins with an exposition of the basic theory of vector spaces and proceeds to explain the fundamental structure theorem for linear maps, including eigenvectors and eigenvalues, quadratic and hermitian forms, diagnolization of symmetric, hermitian, and unitary linear maps and matrices, triangulation, and Jordan canonical form. Material in this new edition has been rewritten and reorganized and new exercises have been added.

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Editorial Reviews

From the Publisher

"The present textbook is intended for a one-term course at the junior or senior level. It begins with an exposition of the basic theory of finite-dimensional vector spaces and proceeds to explain the structure theorems for linear maps, including eigenvectors and eigenvalues, quadratic and Hermitian forms, diagonalization of symmetric, Hermitian, and unitary linear maps and matrices, triangulation, and Jordan canonical form. It also includes a useful chapter on convex sets and the finite-dimensional Krein-Milman theorem. The presentation is aimed at the student who has already had some exposure to the elementary theory of matrices, determinants, and linear maps. In this third edition, many parts of the book have been rewritten and reorganized, and new exercises have been added." (S. Lajos, Mathematical Reviews)

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Product Details

  • ISBN-13: 9781441930811
  • Publisher: Springer New York
  • Publication date: 12/1/2010
  • Series: Undergraduate Texts in Mathematics Series, #1
  • Edition description: Softcover reprint of hardcover 3rd ed. 1987
  • Edition number: 3
  • Pages: 285
  • Product dimensions: 6.10 (w) x 9.20 (h) x 0.80 (d)

Table of Contents

1. Vector Spaces; 2. Matrices; 3. Linear Mappings; 4. Linear Maps and Matrices; 5. Scalar Products and Orthogonality; 6. Determinants; 7. Symmetric, Hermitian, and Unitary Operators; 8. Eigenvectors and Eigenvalues; 9. Polynomials and Matrices; 10. Triangulation of Matrices and Linear Maps; 11. Polynomials and Primary Decomposition; 12. Convex Sets

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Sort by: Showing all of 2 Customer Reviews
  • Posted January 3, 2010

    I Also Recommend:

    Excellent Book for first Book in Linear Algebra

    This book is part of a series of books by Serge Lang for College and Graduate Math Students. It introduces a subject which may be new for a first year student in Mathematics. The writing is clear and the text has many examples.Many schools use it before they teach Calculus. Dr. Lang wrote a full set of undergraduate Calculus Books and Graduate Math Books as well.
    In addition to Linear algebra, he teaches the rudimetns of Set Theory, Theory of Proof, and other subjects that are better placed here, than at the end of Calculus as it used to be. I recommend it for any student who needs to know linear algebra and finds many examples as useful. I think this is an excellent text.

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  • Anonymous

    Posted March 5, 2001

    Not a good choice for a first course

    If you are taking linear algebra for the first time, do not use this book. At most, the information is minimal. It gives the basic theorems and proofs, but little else to help you understand the material. There are not enough practice problems and the explanations are not adequate, in my opinion. I needed this book for my class. I purchased it, realized it wasnt good, returned it, and took a copy from the math dept. Dont buy this book as a learning tool. As a reference, it can serve its purpose. Other than that, look elsewhere.

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