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  • Textbook
  • © 1987

Linear Algebra

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Part of the book series: Undergraduate Texts in Mathematics (UTM)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-ix
  2. Vector Spaces

    • Serge Lang
    Pages 1-22
  3. Matrices

    • Serge Lang
    Pages 23-42
  4. Linear Mappings

    • Serge Lang
    Pages 43-80
  5. Linear Maps and Matrices

    • Serge Lang
    Pages 81-94
  6. Scalar Products and Orthogonality

    • Serge Lang
    Pages 95-139
  7. Determinants

    • Serge Lang
    Pages 140-179
  8. Eigenvectors and Eigenvalues

    • Serge Lang
    Pages 194-230
  9. Polynomials and Matrices

    • Serge Lang
    Pages 231-236
  10. Polynomials and Primary Decomposition

    • Serge Lang
    Pages 245-267
  11. Convex Sets

    • Serge Lang
    Pages 268-276
  12. Back Matter

    Pages 277-296

About this book

Linear Algebra is intended for a one-term course at the junior or senior level. It begins with an exposition of the basic theory of vector spaces and proceeds to explain the fundamental structure theorems for linear maps, including eigenvectors and eigenvalues, quadric and hermitian forms, diagonalization of symmetric, hermitian, and unitary linear maps and matrices, triangulation, and Jordan canonical form. The book 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. However, the book is logically self-contained. In this new edition, many parts of the book have been rewritten and reorganized, and new exercises have been added.

Reviews

"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) 

Authors and Affiliations

  • Department of Mathematics, Yale University, New Haven, USA

    Serge Lang

Bibliographic Information

  • Book Title: Linear Algebra

  • Authors: Serge Lang

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4757-1949-9

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1987

  • Hardcover ISBN: 978-0-387-96412-6Published: 26 January 1987

  • Softcover ISBN: 978-1-4419-3081-1Published: 01 December 2010

  • eBook ISBN: 978-1-4757-1949-9Published: 29 June 2013

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 3

  • Number of Pages: IX, 285

  • Additional Information: Originally published by Addison-Wesley, Reading, 1971

  • Topics: Linear and Multilinear Algebras, Matrix Theory

Buy it now

Buying options

eBook USD 49.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 64.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 64.95
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access