Elementary Linear Algebra 4th Edition by Stephen Andrilli, David Hecker 0123747511 9780123747518

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Product details:

ISBN 10: 0123747511

ISBN 13: 9780123747518

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.

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 Dimension 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

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Tags: Stephen Andrilli, David Hecker, Elementary, Linear