[Book Cover]

Linear Algebra with Applications, 1/e

Otto Bretscher, Harvard University

Published December, 1996 by Prentice Hall Engineering/Science/Mathematics

Copyright 1997, 587 pp.
ISBN 0-13-190729-8

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This introductory text emphasizes linear transformations as a unifying theme. Students are able to do both computational and abstract math in each chapter. This is the most geometric presentation now available. Half way through the text, when eigenvectors are reached, a second theme, on dynamical systems, emerges for the second half of the text. There is also a wider range of problem sets in this text than any other in this market. Free to users is an accompanying website at prenhall.com/bretscher.


Offers a careful sequencing of material — with a focus on smooth transitions and good motivations for new concepts.
Uses visualization and geometrical interpretations extensively throughout, e.g.:

  • The geometrical interpretations of the determinant.
  • The use of phase portraits for dynamical systems.
  • The geometrical interpretations of the QR-factorization and the singular value decomposition.
Avoids the “wall of vector spaces” that often overwhelms and confuses students, leaving them lost and discouraged early in the course.
  • Introduces the abstract concepts gradually and gently throughout the text — and brings up the notion of a vector space (or linear space) only in the last chapter.
Provides an early introduction to linear transformation — to make the discussion of matrix manipulations more meaningful and easier to visualize.
Includes a discussion of phase portraits.
Features a large number of superb problems and exercises, including:
  • Routine problems.
  • Probing, thought-provoking exercises — some abstract and some focusing on applications.
One application —in dynamical systems—runs throughout the text to unify the presentation and provide motivation for readers.
Extensive historical references are found throughout to provide motivation and meaning.

Table of Contents
    1. Linear Equations.
    2. Linear Transformations.
    3. Subspaces of R^n and Their Dimension.
    4. Orthogonality and Least Squares.
    5. Determinants.
    6. Eigenvalues and Eigenvectors.
    7. Coordinate Systems.
    8. Linear Systems of Differential Equations.
    9. Linear Spaces.
    Appendix A. Vectors.
    Answers to Odd-Numbered Exercises.


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