Williams G. Linear Algebra with Applications

N.-Y.: Jones & Bartlett Learning, 2012. - 599p.Updated and revised to increase clarity and further improve student learning, the Eighth Edition of Gareth Williams' classic text is designed for the introductory course in linear algebra. It provides a flexible blend of theory and engaging applications for students within engineering, science, mathematics, business management, and physics. It is organized into three parts that contain core and optional sections. There is then ample time for the instructor to select the material that gives the course the desired flavor. Part 1 introduces the basics, presenting systems of linear equations, vectors and subspaces of Rn, matrices, linear transformations, determinants, and eigenvectors. Part 2 builds on the material presented in Part1 and goes on to introduce the concepts of general vector spaces, discussing properties of bases, developing the rank/nullity theorem, and introducing spaces of matrices and functions. Part 3 completes the course with important ideas and methods of numerical linear algebra, such as ill-conditioning, pivoting, and LU decomposition. Throughout the text the author takes care to fully and clearly develop the mathematical concepts and provide modern applications to reinforce those concepts. The applications range from theoretical applications within differential equations and least square analysis, to practical applications in fields such as archeology, demography, electrical engineering and more. New exercises can be found throughout that tie back to the modern examples in the text.Part Linear Equations, Vectors, and Matrices
Matrices and Systems of Linear Equations
Gauss-Jordan Elimination
The Vector Space Rn
Subspaces of Rn
Basis and Dimension in Rn
Dot Product, Norm, Angle, and Distance
Curve Fitting, Electrical Networks, and Traffic Flow
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
Introduction to Determinants
Properties of Determinants
Determinants, Matrix Inverses, and Systems of Linear Equations
Eigenvalues and Eigenvectors
Google, Demography, Weather Prediction, and Leslie Matrix Models
Part 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
Coordinate Vectors
Matrix Representations of Linear Transformations
Diagonalization of Matrices
Quadratic Forms, Difference Equations, and Normal Modes
Inner Product Spaces
Non-Euclidean Geometry and Special Relativity
Approximation of Functions and Coding Theory
Least Squares Solutions
Appendices
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
A Geometrical Introduction to Linear Programming
The Simplex Method
Geometrical Explanation of the Simplex Method
Appendix A Cross Product
Appendix B Equations of Planes and Lines in Three-Space
Appendix C Graphing Calculator Manual
Appendix D MatLAB Manual
Answers to Selected Exercises