Elementary Linear Algebra: Part III

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184 pages
Language:
 English
This is an introduction to linear algebra. The main part of the book features row operations and everything is done in terms of the row reduced echelon form and specific algorithms.
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About the author

Kenneth Kuttler received his Ph.D. in mathematics from The University of Texas at Austin in 1981. From there, he went to Michigan Tech. University where he was employed for most of the next 17 years. He joined the faculty of Brigham Young University in 1998 and has been there since this time. Kuttler'...

Description
Content

This is an introduction to linear algebra. The main part of the book features row operations and everything is done in terms of the row reduced echelon form and specific algorithms. At the end, the more abstract notions of vector spaces and linear transformations on vector spaces are presented. This is intended to be a first course in linear algebra for students who are sophomores or juniors who have had a course in one variable calculus and a reasonable background in college algebra.

About the author

Kenneth Kuttler received his Ph.D. in mathematics from The University of Texas at Austin in 1981. From there, he went to Michigan Tech. University where he was employed for most of the next 17 years. He joined the faculty of Brigham Young University in 1998 and has been there since this time. Kuttler's research interests are mainly in the mathematical theory for nonlinear initial boundary value problems, especially those which come from physical models that include damage, contact, and friction. Recently he has become interested in stochastic integration and the related problems involving nonlinear stochastic evolution equations.


  1. Vector Spaces
    1. Algebraic Considerations
    2. Exercises
    3. Linear Independence And Bases
    4. Vector Spaces And Fields*
    5. Exercises
  2. Inner Product Spaces
    1. Basic Definitions And Examples
    2. The Gram Schmidt Process
    3. Approximation And Least Squares
    4. Orthogonal Complement
    5. Fourier Series
    6. The Discreet Fourier Transform
    7. Exercises
  3. Linear Transformations
    1. Matrix Multiplication as a Linear Transformation
    2. L(V, W) As A Vector Space
    3. Eigenvalues And Eigenvectors Of Linear Transformations
    4. Block Diagonal Matrices
    5. The Matrix Of A Linear Transformation
    6. The Matrix Exponential, Differential Equations*
    7. Exercises
  • Appendix A
  • The Jordan Canonical Form*
  • Appendix B Directions For Computer Algebra Systems
    • B.1 Finding Inverses
    • B.2 Finding Row Reduced Echelon Form
    • B.3 Finding PLU Factorizations
    • B.4 Finding QR Factorizations
    • B.5 Finding Singular Value Decomposition
    • B.6 Use Of Matrix Calculator On Web
  • Bibliography
  • Appendix C Answers To Selected Exercises
    • C.16 Exercises 508
    • C.17 Exercises 538
    • C.18 Exercises 563
    • C.19 Exercises 611
    • Endnotes
  • Index