Linear Algebra I
Matrices and Row operations
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About the book
Description
This consists of the elementary aspects of linear algebra which depend mainly on row operations involving elementary manipulations of matrices. The field of scalars is typically the field of complex numbers.
Content
 Preface
 Preliminaries
 Sets And Set Notation
 Functions
 The Number Line And Algebra Of The Real Numbers
 Ordered fields
 The Complex Numbers
 Exercises
 Completeness of R
 Well Ordering And Archimedean Property
 Division And Numbers
 Systems Of Equations
 Exercises
 Fn
 Algebra in Fn
 Exercises
 The Inner Product In Fn
 What Is Linear Algebra?
 Exercises
 Matrices And Linear Transformations
 Matrices
 Exercises
 Linear Transformations
 Subspaces And Spans
 An Application To Matrices
 Matrices And Calculus
 Exercises
 Determinants
 Basic Techniques And Properties
 Exercises
 The Mathematical Theory Of Determinants
 The Cayley Hamilton Theorem
 Block Multiplication Of Matrices
 Exercises
 Row Operations
 Elementary Matrices
 The Rank Of A Matrix
 The Row Reduced Echelon Form
 Rank And Existence Of Solutions To Linear Systems
 Fredholm Alternative
 Exercises
 Some Factorizations
 LU Factorization
 Finding An LU Factorization
 Solving Linear Systems Using An LU Factorization
 The PLU Factorization
 Justification For The Multiplier Method
 Existence For The PLU Factorization
 The QR Factorization
 Exercises
 Linear Programming
 Simple Geometric Considerations
 The Simplex Tableau
 The Simplex Algorithm
 Finding A Basic Feasible Solution
 Duality
 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.