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Renowned professor and author Gilbert Strang demonstrates that linear algebra is a fascinating subject by showing both its beauty and applications. While giving you the necessary mathematics, the book is not entirely concentrated on theorems and proofs. Strang explains rather than deduces; the emphasis is on understanding. This book is written in an informal and personal style and teaches real mathematics. In Chapter 2, the gears change as you transition to vector spaces. Throughout the book, the theory is motivated and reinforced by interesting and important applications.
- The exercise sets in the book have been greatly extended and thoroughly updated. They feature many new problems drawn from Professor Strang's extensive teaching experience.
- The writing and the plentiful new examples reflect Gilbert Strang's hallmark clear and lively style.
- New coverage of the Singular Value Decomposition has been added to the text. The row reduced echelon form plays a larger part in the discussion of elimination. The Four Fundamental Subspaces remain central to the understanding of vector spaces in Chapter 2.
- A second color has been added to the illustrations and boxes, many of which are new.
- The Linear Algebra web pages offer review outlines and a full set of video lectures by Gilbert Strang. The site also includes eigenvalue modules with audio (ocw.mit.edu and web.mit.edu/18.06).
- Offers a large number of applications to physics, engineering, probability and statistics, economics, and biology. These are not tacked on at the end; they are part of the mathematics.
- Includes an optional section on the Fast Fourier Transform. Students discover how this outstanding algorithm fits into linear algebra and introduces complex numbers.
- Recognizes what the computer can do in linear algebra, without being dominated by it.
- Contains a wealth of exercises that appear in the sections and in the chapter reviews.
Introduction. The Geometry of Linear Equations. An Example of Gaussian Elimination. Matrix Notation and Matrix Multiplication. Triangular Factors and Row Exchanges. Inverses and Transposes. Special Matrices and Applications. Review Exercises.
2. VECTOR SPACES.
Vector Spaces and Subspaces. The Solution of m Equations in n Unknowns. Linear Independence, Basis, and Dimension. The Four Fundamental Subspaces. Networks and Incidence Matrices. Linear Transformations. Review Exercises.
Perpendicular Vectors and Orthogonal Subspaces. Inner Products and Projections onto Lines. Least Squares Approximations. Orthogonal Bases, Orthogonal Matrices, and Gram-Schmidt Orthogonalization. The Fast Fourier Transform. Review and Preview. Review Exercises.
Introduction. Properties of the Determinant. Formulas for the Determinant. Applications of Determinants. Review Exercises.
5. EIGENVALUES AND EIGENVECTORS.
Introduction. Diagonalization of a Matrix. Difference Equations and the Powers Ak. Differential Equations and the Exponential eAt. Complex Matrices: Symmetric vs. Hermitian. Similarity Transformations. Review Exercises.
6. POSITIVE DEFINITE MATRICES.
Minima, Maxima, and Saddle Points. Tests for Positive Definiteness. The Singular Value Decomposition. Minimum Principles. The Finite Element Method.
7. COMPUTATIONS WITH MATRICES.
Introduction. The Norm and Condition Number. The Computation of Eigenvalues. Iterative Methods for Ax = b.
8. LINEAR PROGRAMMING AND GAME THEORY.
Linear Inequalities. The Simplex Method. Primal and Dual Programs. Network Models. Game Theory.
Appendix A: Computer Graphics.
Appendix B: The Jordan Form.
Solutions to Selected Exercises.
Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.
Student Solutions Manual
Includes detailed step-by-step solutions to selected odd-numbered problems.
Instructor's Solutions Manual
This author-prepared Instructor's Solution Manual contains resources designed to streamline and maximize the effectiveness of your course preparation. It includes worked solutions to all of the exercises in the text. For instructors only.
Student Solutions Manual