Elementary Linear Algebra

We are terribly sorry, but in order to download our books or watch our videos, you will need a browser that allows JavaScript.

You will receive our newsletter regarding Bookboon and Free Books. Any contact details you provide will not be disclosed to any third parties.

You need to have Adobe Reader installed in order to open the books from bookboon.com

Description

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.

Content

  • Preface
  • Some Prerequisite Topics
    1. Sets And Set Notation
    2. Functions
    3. Graphs Of Functions
    4. The Complex Numbers
    5. Polar Form Of Complex Numbers
    6. Roots Of Complex Numbers
    7. The Quadratic Formula
    8. Exercises
  • Fn
    1. Algebra in Fn
    2. Geometric Meaning Of Vectors
    3. Geometric Meaning Of Vector Addition
    4. Distance Between Points In Rn Length Of A Vector
    5. Geometric Meaning Of Scalar Multiplication
    6. Exercises
    7. Vectors And Physics
    8. Exercises
  • Vector Products
    1. The Dot Product
    2. The Geometric Significance Of The Dot Product
    3. Exercises
    4. The Cross Product
    5. The Vector Identity Machine
    6. Exercises
  • Systems Of Equations
    1. Systems Of Equations, Geometry
    2. Systems Of Equations, Algebraic Procedures
    3. Exercises
  • Matrices
    1. Matrix Arithmetic
    2. Exercises
  • Determinants
    1. Basic Techniques And Properties
    2. Applications
    3. A Formula For The Inverse
    4. Cramer’s Rule
    5. Exercises
  • The Mathematical Theory Of Determinants
    1. The Function sgnn
    2. The Determinant
    3. The Cayley Hamilton Theorem
  • Rank Of A Matrix
    1. Elementary Matrices
    2. THE Row Reduced Echelon Form Of A Matrix
    3. The Rank Of A Matrix
    4. Fredholm Alternative
    5. Exercises
  • Linear Transformations
    1. Linear Transformations
    2. Constructing The Matrix Of A Linear Transformation
    3. Exercises
  • 10 The LU Factorization
    1. Definition Of An LU factorization
    2. Finding An LU Factorization By Inspection
    3. Using Multipliers To Find An LU Factorization
    4. Solving Systems Using The LU Factorization
    5. Justification For The Multiplier Method
    6. The PLU Factorization
    7. The QR Factorization
    8. Exercises
  • 1Linear Programming
    1. 1Simple Geometric Considerations
    2. 1The Simplex Tableau
    3. 1The Simplex Algorithm
    4. 1Finding A Basic Feasible Solution
    5. 1Duality
    6. 1Exercises
  • Spectral Theory
    1. Eigenvalues And Eigenvectors Of A Matrix
    2. Some Applications Of Eigenvalues And Eigenvectors
    3. The Estimation Of Eigenvalues
    4. Exercises
  • Matrices And The Inner Product
    1. Symmetric And Orthogonal Matrices
    2. Fundamental Theory And Generalizations
    3. Least Square Approximation
    4. The Right Polar Factorization
    5. The Singular Value Decomposition
    6. Approximation In The Frobenius Norm
    7. Moore Penrose Inverse
    8. Exercises
  • Numerical Methods For Solving Linear Systems
    1. Iterative Methods For Linear Systems
    2. The Operator Norm
    3. The Condition Number
    4. Exercises
  • Numerical Methods For Solving The Eigenvalue Problem
    1. The Power Method For Eigenvalues
    2. The Shifted Inverse Power Method
    3. The Rayleigh Quotient
    4. The QR Algorithm
    5. Exercises
  • Vector Spaces
    1. Algebraic Considerations
    2. Exercises
    3. Vector Spaces And Fields
    4. Exercises
    5. Inner Product Spaces
    6. Exercises
  • 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. Exercises
  • A The Jordan Canonical Form*
  • B The Fundamental Theorem Of Algebra
  • C Answers To Selected Exercises

    • 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.

    Embed Book

    Size
    Choose color
    Implementation code. Copy into your own page

    If you love free textbooks - why not Share the love!