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1. Some Prerequisite Topics 2. Fn 3. Vector Products 4. Systems Of Equations 5. Matrices 6. Determinants 7. The Mathematical Theory Of Determinants 8. Rank Of A Matrix 9. Linear Transformations 10. The LU Factorization 11. Linear Programming 12. Spectral Theory 13. Matrices And The Inner Product 14. Numerical Methods For Solving Linear Systems 15. Numerical Methods For Solving The Eigenvalue Problem 16. Vector Spaces 17. Linear Transformations A. The Jordan Canonical Form* B. The Fundamental Theorem Of Algebra
This is an introduction to linear algebra to be used either before or after an undergraduate course in Calculus. The main part of the book features row operations and everything is done in terms of the row reduced echelon form and specific algorithms. It contains all of the standard topics along with applications to other subjects. All major theorems are completely proved for the sake of any who are interested. Also instructions are given for the use of MATLAB and other computer algebra systems. It provide the complete proofs of all the fundamental ideas but some topics such as Markov matrices are not complete in this book but receive a plausible introduction. At the end, the more abstract notions of vector spaces and linear transformations on vector spaces are presented. However, 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.
Title: Elementary Linear Algebra by Kenneth Kuttler Publisher: The Saylor Foundation Year: 2012 Pages: 443 Type: PDF Language: English ISBN-10 #: B09FC8CLFK ISBN-13 #: 979-8469552338 License: CC BY 3.0 Amazon: Amazon
The author Kenneth Kuttler is Professor in the Department of Mathematics at Brigham Young University. His area of research is Partial Differential Equations and Inclusions. He works on abstract methods for determining and mathematical theory of problems from contact mechanics. He has also been studying extensions to stochastic equations and inclusions.
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