Linear Algebra and Its Applications
- 2nd Edition - January 1, 1980
- Imprint: Academic Press
- Author: Gilbert Strang
- Language: English
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 6 5 1 1 - 7
Linear Algebra and Its Applications, Second Edition fulfills the need for a book that will permit the teaching of the applications of linear algebra, in combination with the… Read more
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Request a sales quoteLinear Algebra and Its Applications, Second Edition fulfills the need for a book that will permit the teaching of the applications of linear algebra, in combination with the underlying mathematics. Comprised of eight chapters, the book aims to provide a comprehensive presentation of the concepts and methods in linear algebra. The text starts with the discussion of the Gaussian elimination, the simplest and most useful method of solution. This chapter is followed by chapters that focus on the study of vector spaces, projections and inner products, determinants, and eigenvalues. Discussions on positive definite matrices, computations with matrices, and introduction to linear programming and game theory are provided as well. This text is intended for use by college students.
Preface
1 Gaussian Elimination
1.1 Introduction
1.2 An Example of Gaussian Elimination
1.3 Matrix Notation and Matrix Multiplication
1.4 Gaussian Elimination = Triangular Factorization
1.5 Row Exchanges, Inverses, and Transposes
1.6 Band Matrices, Applications, and Roundoff
Review Exercises
2 The Theory of Simultaneous Linear Equations
2.1 Vector Spaces and Subspaces
2.2 The Solution of m Equations in η Unknowns
2.3 Linear Independence, Basis, and Dimension
2.4 The Four Fundamental Subspaces
2.5 Orthogonality of Vectors and Subspaces
2.6 Pairs of Subspaces and Products of Matrices
Review Exercises
3 Orthogonal Projections and Least Squares
3.1 Inner Products and Projections onto Lines
3.2 Projections onto Subspaces and Least Squares Approximations
3.3 Orthogonal Bases, Orthogonal Matrices, and Gram-Schmidt Orthogonalization
3.4 The Pseudoinverse and the Singular Value Decomposition
3.5 Weighted Least Squares
Review Exercises
4 Determinants
4.1 Introduction
4.2 The 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 The Diagonal Form of a Matrix
5.3 Difference Equations and the Powers Ak
5.4 Differential Equations and the Exponential eAT
5.5 The Complex Case: Hermitian and Unitary Matrices
5.6 Similarity Transformations and Triangular Forms
Review Exercises
6 Positive Definite Matrices
6.1 Minima, Maxima, and Saddle Points
6.2 Tests for Positive Definiteness
6.3 Semidefinite and Indefinite Matrices; Ax = λBx
6.4 Minimum Principles and Rayleigh's Quotient
6.5 The Rayleigh- Ritz Principle and Finite Elements
7 Computations with Matrices
7.1 Introduction
7.2 The Norm and Condition Number of a Matrix
7.3 The 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 Theory of Duality
8.4 Network Models
8.5 Game Theory and the Minimax Theorem
Appendix A Linear Transformations, Matrices, and Change of Basis
Appendix Β The Jordan Form
Appendix C Computer Codes for Linear Algebra
References
Solutions to Exercises
Index
- Edition: 2
- Published: January 1, 1980
- Imprint: Academic Press
- No. of pages: 428
- Language: English
- eBook ISBN: 9781483265117
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