## Description

Elementary develops and explains in careful detail the computational techniques and fundamental theoretical results central to a 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.

includes a wide variety of applications, technology tips and exercises, organized in chart format for easy reference. More than 310 numbered examples in the text at least one for each new concept or application.

Exercise sets ordered by increasing difficulty, many with multiple parts for a total of more than 2135 questions. Provides an early introduction to /eigenvectors. A Student manual, containing fully worked out solutions and instructors manual available.

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• Chapter 1: Vectors and Matrices
Section 1.1: Fundamental Operations with Vectors
Section 1.2: The Dot Product
Section 1.3: An Introduction to Proof Techniques
Section 1.4: Fundamental Operations with Matrices
Section 1.5: Matrix Multiplication

Chapter 2: Systems of Linear Equations
Section 2.1: Solving Linear Systems Using Gaussian Elimination
Section 2.2: Gauss-Jordan Row Reduction and Reduced Row Echelon Form
Section 2.3: Equivalent Systems, Rank, and Row Space
Section 2.4: Inverses of Matrices

Chapter 3: Determinants and Eigenvalues
Section 3.1: Introduction to Determinants
Section 3.2: Determinants and Row Reduction
Section 3.3: Further Properties of the Determinant
Section 3.4: Eigenvalues and Diagonalization
Summary of Techniques

Chapter 4: Finite Dimensional Vector Spaces
Section 4.1: Introduction to Vector Spaces
Section 4.2: Subspaces
Section 4.3: Span
Section 4.4: Linear Independence
Section 4.5: Basis and Dimension
Section 4.6: Constructing Special Bases
Section 4.7: Coordinatization

Chapter 5: Linear Transformations
Section 5.1: Introduction to Linear Transformations
Section 5.2: The Matrix of a Linear Transformation
Section 5.3: The Dimension Theorem
Section 5.4: Isomorphism
Section 5.5: Diagonalization of Linear Operators

Chapter 6: Orthogonality
Section 6.1: Orthogonal Bases and the Gram-Schmidt Process
Section 6.2: Orthogonal Complements
Section 6.3: Orthogonal Diagonalization

Chapter 7: Complex Vector Spaces and General Inner Products
Section 7.1: Complex n-Vectors and Matrices
Section 7.2: Complex Eigenvalues and Eigenvectors
Section 7.3: Complex Vector Spaces
Section 7.4: Orthogonality in Cn
Section 7.5: Inner Product Spaces

Section 8.1: Graph Theory
Section 8.2: Ohm's Law
Section 8.3: Least-Squares Polynomials
Section 8.4: Markov Chains
Section 8.5: Hill Substitution: An Introduction to Coding Theory
Section 8.6: Change of Variables and the Jacobian
Section 8.7: Rotation of Axes
Section 8.8: Computer Graphics
Section 8.9: Differential Equations
Section 8.10: Least-Squares Solutions for Inconsistent Systems
Section 8.11: Max-Min Problems in Rn and the Hessian Matrix

Chapter 9: Numerical Methods
Section 9.1: Numerical Methods for Solving Systems
Section 9.2: LDU Decomposition
Section 9.3: The Power Method for Finding Eigenvalues

Chapter 10: Further Horizons
Section 10.1: Elementary Matrices
Section 10.2: Function Spaces

Appendix A: Miscellaneous Proofs
Appendix B: Functions
Appendix C: Complex Numbers
Appendix D: Computers and Calculators
Appendix E: Answers to Selected Exercises
• Citation Inline Feedbacks Pankaj Goswami
12/09/2016 6:43 pm

Really good book with cool content. Would totally recommend this web site to my friends. Pankaj Goswami
12/09/2016 6:46 pm

What I expected. thank you

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