Linear algebra with applications

This book includes an index

Chapter 1: Linear Equations and Vectors • Matrices and Systems of Linear Equations • Gauss-Jordan Elimination • The Vector Space Rn • Subspaces of Rn • Basis and Dimension • Dot Product, Norm, Angle, and Distance (Option: This section can be deferred to just before Section 4.6.) • Curve Fitting, Electrical Networks, and Traffic Flow • Chapter 1 Review Exercises Chapter 2: Matrices and Linear Transformations • Addition, Scalar Multiplication, and Multiplication of Matrices • Properties of Matrix Operations • Symmetric Matrices and Seriation in Archaeology • The Inverse of a Matrix and Cryptography • Matrix Transformations, Rotations, and Dilations • Linear Transformations, Graphics, and Fractals • The Leontief Input-Output Model in Economics • Markov Chains, Population Movements, and Genetics • A Communication Model and Group Relationships in Sociology • Chapter 2 Review Exercises Chapter 3: Determinants and Eigenvectors • Introduction to Determinants • Properties of Determinants • Determinants, Matrix Inverses, and Systems of Linear Equations • Eigenvalues and Eigenvectors (Option: Diagonalization of Matrices, Section 5.3, may be discussed at this time.) • Google, Demography, Weather Prediction, and Leslie Matrix Models • Chapter 3 Review Exercises Chapter 4: General Vector Spaces • General Vector Spaces and Subspaces • Linear Combinations of Vectors • Linear Independence of Vectors • Properties of Bases • Rank • Projections, Gram-Schmidt Process, and QR Factorization • Orthogonal Complement • Kernel, Range, and the Rank/Nullity Theorem • One-to-One Transformations and Inverse Transformations • Transformations and Systems of Linear Equations • Chapter 4 Review Exercises Chapter 5: Coordinate Representations • Coordinate Vectors • Matrix Representations of Linear Transformations • Diagonalization of Matrices • Quadratic Forms, Difference Equations, and Normal Modes • Linear Differential Equations (Calculus Prerequisite) • Chapter 5 Review Exercises Chapter 6: Inner Product Spaces • Inner Product Spaces • Non-Euclidean Geometry and Special Relativity • Approximation of Functions and Coding Theory • Least Squares Solutions • Chapter 6 Review Exercises Chapter 7: Numerical Methods • Gaussian Elimination • The Method of LU Decomposition • Practical Difficulties in Solving Systems of Equations • Iterative Methods for Solving Systems of Linear Equations • Eigenvalues by Iteration and Connectivity of Networks • The Singular Value Decomposition • Chapter 7 Review Exercises Chapter 8: Linear Programming • A Geometrical Introduction to Linear Programming • The Simplex Method • Geometrical Explanation of the Simplex Method • Chapter 8 Review Exercises

Linear Algebra with Applications, Ninth Edition is designed for the introductory course in linear algebra for students within engineering, mathematics, business management, and physics. Updated to increase clarity and improve student learning, the author provides a flexible blend of theory and engaging applications.