Álgebra Lineal Elemental – S. Andrilli, D. Hecker – 4ta Edición

Descripción

Álgebra Lineal Elemental desarrolla y explica con detalle las computacionales y los resultados teóricos fundamentales para un primer curso de Álgebra Lineal. Este aclamado texto se centra en el abstracto, esencial para el estudio .

Los autores dan atención temprana e intensiva a las habilidades necesarias para hacer que los estudiantes se sientan cómodos con las pruebas . Además, el texto construye una transición gradual y suave de los resultados computacionales para la teoría general de espacios vectoriales abstractos. También proporciona cobertura flexible de aplicaciones prácticas, explorando una amplia gama de temas.

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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
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