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328 pages

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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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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.

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.

- Preface

- Some Prerequisite Topics
- Sets And Set Notation
- Well Ordering And Induction
- The Complex Numbers
- Polar Form Of Complex Numbers
- Roots Of Complex Numbers
- The Quadratic Formula
- The Complex Exponential
- The Fundamental Theorem Of Algebra
- Exercises

- Fn
- Algebra in Fn
- Geometric Meaning Of Vectors
- Geometric Meaning Of Vector Addition
- Distance Between Points In Length Of A Vector
- Geometric Meaning Of Scalar Multiplication
- Parametric Lines
- Exercises
- Vectors And Physics
- Exercises

- Vector Products
- The Dot Product
- The Geometric Significance Of The Dot Product
- Exercises
- The Cross Product
- The Vector Identity Machine
- Exercises

- Systems Of Equations
- Systems Of Equations, Geometry
- Systems Of Equations, Algebraic Procedures
- MATLAB And Row Reduced Echelon Form
- Exercises

- Matrices
- Matrix Arithmetic
- MATLAB And Matrix Arithmetic
- Exercises

- Determinants
- Basic Techniques And Properties
- Applications
- MATLAB And Determinants
- Exercises

- The Mathematical Theory Of Determinants*
- The Determinant
- The Cayley Hamilton Theorem*

- Rank Of A Matrix
- Elementary Matrices
- THE Row Reduced Echelon Form of A Matrix
- The Rank of A Matrix
- A Short Application To Chemistry
- Linear Independence and Bases
- Fredholm Alternative
- Exercises

- Linear Transformations
- Linear Transformations
- Constructing The Matrix Of A Linear Transformation
- Exercises

- Bibliography
- Appendix C Answers To Selected Exercises
- C.1 Exercises 28
- C.2 Exercises 51
- C.3 Exercises 67
- C.4 Exercises 82
- C.5 Exercises 114
- C.6 Exercises 150
- C.7 Exercises 178
- C.8 Exercises 262
- C.9 Exercises 291

- Endnotes
- Index