- 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
- 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 Systems of Linear Equations—Theoretical Aspects
- 3.4 Systems of Linear Equations—Computational Aspects Systems of Linear Equations—Computational Aspects
- Index of Definitions for Chapter 3
- 4 Determinants
- 5 Diagonalization
- 6 Inner Product Spaces
- 6.7* The Singular Value Decomposition and the Pseudoinverse
- 6.9* Einstein’s Special Theory of Relativity 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
Section 6.9
5.
(Bv)−1=⎛⎝⎜⎜⎜⎜⎜⎜11−v2−−−−−√0v1−v2−−−−−√010v1−v2−−−−−√011−v2−−−−−√⎞⎠⎟⎟⎟⎟⎟⎟
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