Elementary Linear Algebra – Stephen Andrilli, David Hecker – 4th Edition

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Elementary 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 study. The authors give early, intensive attention to the skills necessary to make 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, 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 eigenvalues/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

    Chapter 8: Additional Applications
    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
    Section 10.3: Quadratic Forms

    Appendix A: Miscellaneous Proofs
    Appendix B: Functions
    Appendix C: Complex Numbers
    Appendix D: Computers and Calculators
    Appendix E: Answers to Selected Exercises
  • Citation

Download now Elementary Linear Algebra

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Pankaj Goswami
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
Pankaj Goswami
12/09/2016 6:46 pm

What I expected. thank you

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