With a highly applied and computational focus, this book combines the important underlying theory with examples from electrical engineering, computer science, physics, biology and economics. An expanded list of computer codes in an appendix and more computer-solvable exercises in the text reflect Strang?s interest in computational linear algebra. Many exercises appear in the sections and in the chapter reviews. Exercises are simple but instructive. 

1. MATRICES AND GAUSSIAN ELIMINATION.

1.1 Introduction.

1.2 The Geometry of Linear Equations.

1.3 An Example of Gaussian Elimination.

1.4 Matrix Notation and Matrix Multiplication.

1.5 Triangular Factors and Row Exchanges.

1.6 Inverses and Transposes.

1.7 Special Matrices and Applications. Review Exercises.

2. VECTOR SPACES.

2.1 Vector Spaces and Subspaces.

2.2 Solving Ax=0 and Ax=b.

2.3 Linear Independence, Basis, and Dimension.

2.4 The Four Fundamental Subspaces.

2.5 Graphs and Networks

2.6 Linear Transformations. Review Exercises.

3. ORTHOGONALITY.

3.1 Perpendicular Vectors and Orthogonal Subspaces.

3.2 Inner Products and Projections onto Lines..

3.3 Projections and Linear Squares

3.4 Orthogonal Bases and Gram-Schmidt

3.5 The Fast Fourier Transform. Review Exercises.

4. DETERMINANTS.

4.1 Introduction.

4.2 Properties of the Determinant.

4.3 Formulas for the Determinant.

4.4 Applications of Determinants. Review Exercises.

5. EIGENVALUES AND EIGENVECTORS.

5.1 Introduction.

5.2 Diagonalization of a Matrix.

5.3 Difference Equations and the Powers Ak.

5.4 Differential Equations and eAt.

5.5 Complex Matrices:

5.6 Similarity Transformations. Review Exercises.

6. POSITIVE DEFINITE MATRICES.

6.1 Minima, Maxima, and Saddle Points.

6.2 Tests for Positive Definiteness.

6.3 Singular Value Decomposition.

6.4 Minimum Principles.

6.5 The Finite Element Method.

7. COMPUTATIONS WITH MATRICES.

7.1 Introduction.

7.2 The Norm and Condition Number.

7.3 Computation of Eigenvalues.

7.4 Iterative Methods for Ax = b.

8. LINEAR PROGRAMMING AND GAME THEORY.

8.1 Linear Inequalities.

8.2 The Simplex Method.

8.3 The Dual Programs.

8.4 Network Models.

8.5 Game Theory.

Appendix A: Computer Graphics.

Appendix B: The Jordan Form.

References.

Solutions to Selected Exercises.

Matrix Factorizations Glossary MATLAB teaching Codes Index.

Gilbert Strang

Gilbert Strang is Professor of Mathematics at the Massachusetts Institute of Technology and an Honorary Fellow of Balliol College. He was an undergraduate at MIT and a Rhodes Scholar at Oxford. His doctorate was from UCLA and since then he has taught at MIT. He has been a Sloan Fellow and a Fairchild Scholar and is a Fellow of the American Academy of Arts and Sciences. Professor Strang has published a monograph with George Fix, "An Analysis of the Finite Element Method", and has authored six widely used textbooks. He served as President of SIAM during 1999 and 2000 and he is Chair of the U.S. National Committee on Mathematics for 2003-2004. --This text refers to an out of print or unavailable edition of this title.

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