An edition of Elementary Linear Algebra
(2013)
Elementary Linear Algebra
by Kenneth Kuttler
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Last edited by Alice Kirk
June 25, 2015 | History
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.
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Publish Date
2013
Publisher
Bookboon.com
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Book Details
Table of Contents
Content
1. Some Prerequisite Topics
1.1. Sets And Set Notation
1.2. Functions
1.3. Graphs Of Functions
1.4. The Complex Numbers
1.5. Polar Form Of Complex Numbers
1.6. Roots Of Complex Numbers
1.7. The Quadratic Formula
1.8. Exercises
2. Fn
2.1. Algebra in Fn
2.2. Geometric Meaning Of Vectors
2.3. Geometric Meaning Of Vector Addition
2.4. Distance Between Points In Rn Length Of A Vector
2.5. Geometric Meaning Of Scalar Multiplication
2.6. Exercises
2.7. Vectors And Physics
2.8. Exercises
3. Vector Products
3.1. The Dot Product
3.2. The Geometric Significance Of The Dot Product
3.3. Exercises
3.4. The Cross Product
3.5. The Vector Identity Machine
3.6. Exercises
4. Systems Of Equations
4.1. Systems Of Equations, Geometry
4.2. Systems Of Equations, Algebraic Procedures
4.3. Exercises
5. Matrices
5.1. Matrix Arithmetic
5.2. Exercises
6. Determinants
6.1. Basic Techniques And Properties
6.2. Applications
6.3. Exercises
7. The Mathematical Theory Of Determinants
7.1. The Function sgnn
7.2. The Determinant
7.3. The Cayley Hamilton Theorem
8. Rank Of A Matrix
8.1. Elementary Matrices
8.2. THE Row Reduced Echelon Form Of A Matrix
8.3. The Rank Of A Matrix
8.4. Fredholm Alternative
8.5. Exercises
9. Linear Transformations
9.1. Linear Transformations
9.2. Constructing The Matrix Of A Linear Transformation
9.3. Exercises
10. The LU Factorization
10.1. Definition Of An LU factorization
10.2. Finding An LU Factorization By Inspection
10.3. Using Multipliers To Find An LU Factorization
10.4. Solving Systems Using The LU Factorization
10.5. Justification For The Multiplier Method
10.6. The PLU Factorization
10.7. The QR Factorization
10.8. Exercises
11. Linear Programming
11.1. Simple Geometric Considerations
11.2. The Simplex Tableau
11.3. The Simplex Algorithm
11.4. Finding A Basic Feasible Solution
11.5. Duality
11.6. Exercises
12. Spectral Theory
12.1. Eigenvalues And Eigenvectors Of A Matrix
12.2. Some Applications Of Eigenvalues And Eigenvectors
12.3. The Estimation Of Eigenvalues
12.4. Exercises
13. Matrices And The Inner Product
13.1. Symmetric And Orthogonal Matrices
13.2. Fundamental Theory And Generalizations
13.3. Least Square Approximation
13.4. The Right Polar Factorization
13.5. The Singular Value Decomposition
13.6. Approximation In The Frobenius Norm
13.7. Moore Penrose Inverse
13.8. Exercises
14. Numerical Methods For Solving Linear Systems
14.1. Iterative Methods For Linear Systems
14.2. The Operator Norm
14.3. The Condition Number
14.4. Exercises
15. Numerical Methods For Solving The Eigenvalue Problem
15.1. The Power Method For Eigenvalues
15.2. The Shifted Inverse Power Method
15.3. The Rayleigh Quotient
15.4. The QR Algorithm
15.5. Exercises
15.6. Vector Spaces
15.6.1. Algebraic Considerations
15.6.2. Exercises
15.6.3. Vector Spaces And Fields
15.6.4. Exercises
15.6.5. Inner Product Spaces
15.6.6. Exercises
15.7. Linear Transformations
15.7.1. Matrix Multiplication As A Linear Transformation
15.7.2. L(V,W) As A Vector Space
15.7.3. Eigenvalues And Eigenvectors Of Linear Transformations
15.7.4. Block Diagonal Matrices
15.7.5. The Matrix Of A Linear Transformation
15.7.6. Exercises
15.8. The Jordan Canonical Form*
15.9. The Fundamental Theorem Of Algebra
15.10. Answers To Selected Exercises
ID Numbers
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| June 25, 2015 | Edited by Alice Kirk | Edited without comment. |
| June 25, 2015 | Created by Alice Kirk | Added new book. |