For courses in Advanced Linear Algebra. Illustrates the power of linear algebra through practical applications. This acclaimed theorem-proof text presents a careful treatment of the principal topics of linear algebra. It emphasizes the symbiotic relationship between linear transformations and matrices, but states theorems in the more general infinite-dimensional case where appropriate. Applications to such areas as differential equations, economics, geometry, and physics appear throughout, and can be included at the instructor's discretion.
Author(s): Stephen H. Friedberg; Arnold J. Insel; Lawrence E. Spence
Edition: 5
Publisher: Pearson
Year: 2019
Language: English
Commentary: REUPLOAD of ID 2789063; added bookmarks, compressed the file. Unlike ID 2532221, this maintains a higher quality without blurred pages.
Pages: 612
Contents
Preface
To the Student
1 - Vector Spaces
1.1 Introduction
1.2 Vector Spaces
1.3 Subspaces
1.4 Linear Combinations and Systems of Linear Equations
1.5 Linear Dependence and Linear Independence
1.6 Bases and Dimension
1.7 Maximal Linearly Independent Subsets
2 - Linear Transformations and Matrices
2.1 Linear Transformations, Null spaces, and Ranges
2.2 The Matrix Representation of a Linear Transformation
2.3 Composition of Linear Transformations and Matrix Multiplication
2.4 Invertibility and Isomorphisms
2.5 The Change of Coordinate Matrix
2.6 Dual Spaces
2.7 Homogeneous Linear Differential Equations with Constant Coefficients
3 - Elementary Matrix Operations and Systems of Linear Equations
3.1 Elementary Matrix Operations and Elementary Matrices
3.2 The Rank of a Matrix and Matrix Inverses
3.3 Systems of Linear Equations — Theoretical Aspects
3.4 Systems of Linear Equations — Computational Aspects
4 - Determinants
4.1 Determinants of Order 2
4.2 Determinants of Order n
4.3 Properties of Determinants
4.4 Summary—Important Facts About Determinants
4.5 A Characterization of the Determinant
5 - Diagonalization
5.1 Eigenvalues and Eigenvectors
5.2 Diagonalizability
5.3 Matrix Limits and Markov Chains
5.4 Invariant Subspaces and the Cayley-Hamilton Theorem
6 - Inner Product Spaces
6.1 Inner Products and Norms
6.2 The Gram-Schmidt Orthogonalization Process and Orthogonal Complements
6.3 The Adjoint of a Linear Operator
6.4 Normal and Self-Adjoint Operators
6.5 Unitary and Orthogonal Operators and Their Matrices
6.6 Orthogonal Projections and the Spectral Theorem
6.7 The Singular Value Decomposition and the Pseudoinverse
6.8 Bilinear and Quadratic Forms
6.9 Einstein's Special Theory of Relativity
6.10 Conditioning and the Rayleigh Quotient
6.11 The Geometry of Orthogonal Operators
7 - Canonical Forms
7.1 The Jordan Canonical Form I
7.2 The Jordan Canonical Form II
7.3 The Minimal Polynomial
7.4 The Rational Canonical Form
Appendices
Appendix A - Sets
Appendix B - Functions
Appendix C - Fields
Appendix D - Complex Numbers
Appendix E - Polynomials
Answers to Selected Exercises
Index
List of Symbols
