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

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