Elementary Linear Algebra 4th edition by Stephen Andrilli, David Hecker – Ebook PDF Instant Download/Delivery: 0080886251, 9780080886251
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Product details:
ISBN 10: 0080886251
ISBN 13: 9780080886251
Author: Stephen Andrilli, David Hecker
Elementary Linear Algebra develops and explains in careful detail the computational techniques and fundamental theoretical results central to a first course in linear algebra. This highly acclaimed text focuses on developing the abstract thinking essential for further mathematical study
The authors give early, intensive attention to the skills necessary to make students comfortable with mathematical proofs. The text builds a gradual and smooth transition from computational results to general theory of abstract vector spaces. It also provides flexbile coverage of practical applications, exploring a comprehensive range of topics.
Elementary Linear Algebra 4th Table of contents:
Chapter 1 Vectors and Matrices
1.1 Fundamental Operations with Vectors
1.2 The Dot Product
1.3 An Introduction to Proof Techniques
1.4 Fundamental Operations with Matrices
1.5 Matrix Multiplication
Chapter 2 Systems of Linear Equations
2.1 Solving Linear Systems Using Gaussian Elimination
2.2 Gauss-Jordan Row
2.3 Equivalent Systems, Rank, and Row Space
2.4 Inverses of Matrices
Chapter 3 Determinants and Eigenvalues
3.1 Introduction to Determinants
3.2 Determinants and Row Reduction
3.3 Further Properties of the Determinant
3.4 Eigenvalues and Diagonalization
Chapter 4 Finite Dimensional Vector Spaces
4.1 Introduction to Vector Spaces
4.2 Subspaces
4.3 Span
4.4 Linear Independence
4.5 Basis and Dimension
4.6 Constructing Special Bases
4.7 Coordinatization
Chapter 5 Linear Transformations
5.1 Introduction to Linear Transformations
5.2 The Matrix of a Linear Transformation
5.3 The Dimesion Theorem
5.4 One to One and Onto Linear Transformations
5.5 Isomorphism
5.6 Diagonalization of Linear Operators
Chapter 6 Orthogonality
6.1 Orthogonal Bases
6.2 Orthogonal Complements
6.3 Orthogonal Diagonalization
Chapter 7 Complex Vector Spaces
7.1 Complex n Vectors and Matrices
7.2 Complex Eigenvalues and Complex Eigenvectors
7.3 Complex Vector Spaces
7.4 ORTHOGONALITY IN Cn
7.5 Inner Product Spaces
Chapter 8 Additional Applications
8.1 Graph Theory
8.2 Ohm’s Law
8.3 Least Squares Polynomials
8.4 Markov Chains
8.5 Hill Substitution
8.6 Elementary Matrices
8.7 Rotation of Axes for Conic Sections
8.8 Computer Graphics
8.9 Differential Equations
8.10 Least Squares Solutions
8.11 Quadratic Forms
Chapter 9 Numerical Methods
9.1 Numerical Methods for Solving Systems
9.2 LDU Decomposition
9.3 The Power Method for Finding Eigenvalues
9.4 QR Factorization
9.5 Singular Value Decomposition
Appendix A Miscellaneous Proofs
Appendix B Functions
Appendix C Complex Numbers
Appendix D Answers to Selected Exercises
Index
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