线性代数引论(英文影印版.原书第5版)

3.3 Examples of Subspaces
3.4 Bases for Subspaces
3.5 Dimension
3.6 Orthogonal Bases for Subspaces
3.7 Linear Transformations from Rn to Rm
3.8 Least-Squares Solutions to Inconsistent Systems, with Applications to Data Fitting
3.9 Theory and Practice of Least Squares
4 THE EIGENVALUE PROBLEM
4.1 The Eigenvalue Problem for (2 x 2) Matrices
4.2 Determinants and the Eigenvalue Problem
4.3 Elementary Operations and Determinants (Optional)
4.4 Eigenvalues and the Characteristic Polynomial
4.5 Eigenvectors and Eigenspaces
4.6 Complex Eigenvalues and Eigenvectors ..
4.7 Similarity Transformations and Diagonalization
4.8 Difference Equations; Markov Chains; Systems of Differential Equations (Optional)
5 VECTOR SPACES AND LINEAR TRANSFORMATIONS
5.1 Introduction
5.2 Vector Spaces
5.3 Subspaces
5.4 Linear Independence, Bases, and Coordinates
5.5 Dimension
5.6 Inner-Product Spaces, Orthogonal Bases, and Projections (Optional)
5.7 Linear Transformations
5.8 Operations with Linear Transformations
5.9 Matrix Representations for Linear Transformations
5.10 Change of Basis and Diagonalization
6 DETERMINANTS
6.1 Introduction
6.2 Cofactor Expansions of Determinants
6.3 Elementary Operations and Determinants
6.4 Cramer's Rule
6.5 Applications of Determinants: Inverses and Wronksians
7 EIGENVALUES AND APPLICATIONS
7.1 Quadratic Forms
7.2 Systems of Differential Equations
7.3 Transformation to Hessenberg Form
7.4 Eigenvalues of Hessenberg Matrices
7.5 Householder Transformations
7.6 The QR Factorization and Least-Squares Solutions
7.7 Matrix Polynomials and the Cayley-Hamilton Theorem
7.8 Generalized Eigenvectors and Solutions of Systems of Differential Equations
APPENDIX: AN INTRODUCTION TO MATLAB
ANSWERS TO SELECTED ODD-NUMBERED EXERCISES
INDEX
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