Book description
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.
Table of contents
- Linear Algebra
- Contents
- Preface
- To the Student
- 1 Vector Spaces
-
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
- Index of Definitions for Chapter 2
- 3 Elementary Matrix Operations and Systems of Linear Equations
- 4 Determinants
- 5 Diagonalization
-
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
- Index of Definitions for Chapter 6
- 7 Canonical Forms
- Appendices
- Answers to Selected Exercises
- Index
- List of Symbols
Product information
- Title: Linear Algebra, 5th Edition
- Author(s):
- Release date: September 2018
- Publisher(s): Pearson
- ISBN: 9780136745495
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