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This book provides an introduction to the basic ideas, computational techniques, and applications of linear algebra. KEY TOPICS: Introductory Linear Algebra with Applications Sixth Edition emphasizes the computational and geometrical aspects of linear algebra, while keeping abstraction to a minimum and illustrating every idea with examples. It provides three different types of exercises. Exercises contains routine exercises. Theoretical Exercises includes exercises that fill in gaps in some of the proofs and can be used to challenge the more capable and interested reader. The third class consists of MATLAB exercises connected to the available MATLAB disk. In addition, the end of every chapter contains a summary of Key Ideas for Review, a set of Supplementary Exercises, and a Chapter Test. The sixth edition of Introductory Linear Algebra with Applications has been revised to incorporate recommendations from The Linear Algebra Curriculum Study Group on developing ways to improve instruction in linear algebra. A valuable reference book on the basic of linear algebra and its applications for any reader seeking information on the subject.

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• I Introductory Linear Algebra
• 1 Linear Equations and Matrices
• Linear Systems
• Matrices
• Dot Product and Matrix Multiplication
• Properties of Matrix Operations
• Graph Theory (Optional)
• Solutions of Linear Systems of Equations
• Electrical Circuits (Optional)
• Markov Chains (Optional)
• The Inverse of a Matrix
• Linear Economic Models (Optional)
• Wavelets (Optional)
• LU-Factorization (Optional)
• 2 Determinants
• Definition and Properties
• Cofactor Expansion and Applications
• Determinants from a Computational Point of View
• 3 Vectors in R2 and R3
• Vectors in the Plane
• N-Vectors
• Introduction to Linear Transformations
• Computer Graphics
• Computer Graphics (Optional)
• Cross Products in R3 (Optional)
• Lines and Planes
• 4 Real Vector Spaces
• Real Vector Spaces
• Subspaces
• Linear Independence
• Basis and Dimension
• Homogeneous Systems
• The Rank of a Matrix and Applications
• Coordinates and Change of Basis
• Orthonormal Bases in Rn
• QR-Factorization (Optional)
• Orthogonal Complements
• Least Squares (Optional)
• 5 Eigenvalues and Eigenvectors
• Eigenvalues and Eigenvectors
• Diagonalization and Similar Matrices
• Diagonalization and Symmetric Matrices
• 6 Linear Transformations and Matrices
• Definition and Examples
• The Kernel and Range of a Linear Transformation
• The Matrix of a Linear Transformation
• Cumulative Review of Part I
• II OTHER APPLICATIONS
• 7 Linear Programming
• The Linear Programming Problem
• Geometric Solution
• The Simplex Method
• Duality
• The Theory of Games
• 8 Applications of Eigenvalues and Eigenvectors
• The Fibonacci Sequence
• Differential Equations (Calculus Required)
• Dynamical Systems (Calculus Required)
• Intro to Fractals
• Quadratic Forms
• Conic Sections
• Quadric Surfaces
• Appendix A Introduction to MATLAB
• Appendix B Complex Numbers
• Complex Numbers
• Complex Numbers in Linear Algebra
• Appendix C Further Directions
• Inner Product Spaces (Calculus Required)
• Composite and Invertible Linear Transformations
• Answers to Odd-Numbered Exercises and Chapter Tests
• Index