This book not only covers up (practically all) basic concepts of Linear Algebra but also educates the reader its applications to Optimization, graph theory, game theory, etc. This book should be a primer to anyone who wishes to pursue subjects related to Computational sciences, Operational Research, or any topic in Computer Science and Applied (or Abstract) Mathematics. Prof. Gilbert Strang with his method of communication really motivates the reader to pursue Algebra and read about subjects not covered in detail in this book.
Book Summary of Linear Algebra And Its Applications
Renowned professor and author Gilbert Strang demonstrates that linear algebra is a fascinating
subject by showing both its beauty and value. While the mathematics is there, the effort is not
all concentrated on proofs. Strang's emphasis is on understanding. He explains concepts, rather
than deduces. This book is written in an informal and personal style and teaches real mathematics.
The gears change in Chapter 2 as students reach the introduction of vector spaces. Throughout
the book, the theory is motivated and reinforced by genuine applications, allowing pure
mathematicians to teach applied mathematics.
Features
- The exercise sets in the book have been extensively updated. They feature many new
- problems from Professor Strang's long experience.
- New coverage of the Singular Value Decomposition has been added to the text.*
- A second color has been added to the illustrations and boxes, many of which are new.
- 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.
Table of Contents
- 1. MATRICES AND GAUSSIAN ELIMINATION. 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.
- 3. ORTHOGONALITY. 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.
- 4. DETERMINANTS. 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.
Details of Book: Linear Algebra And Its Applications
| Book: | Linear Algebra And Its Applications |
| Author: | Gilbert Strang |
| ISBN: | 8131501728 |
| ISBN-13: | 9788131501726,978-8131501726 |
| Binding: | Paperback |
| Publishing Date: | 2007 |
| Publisher: | Nelson Engineering |
| Edition: | 4thEdition |
| Number of Pages: | Paperback |
| Language: | English |
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