Page 15 - A Course in Linear Algebra with Applications
P. 15
xiv Contents
Chapter Four Introduction to Vector Spaces
4.1 Examples of Vector Spaces 87
4.2 Vector Spaces and Subspaces 95
4.3 Linear Independence in Vector Spaces 104
Chapter Five Basis and Dimension
5.1 The Existence of a Basis 112
5.2 The Row and Column Spaces of a Matrix 126
5.3 Operations with Subspaces 133
Chapter Six Linear Transformations
6.1 Functions Defined on Sets 152
6.2 Linear Transformations and Matrices 158
6.3 Kernel, Image and Isomorphism 178
Chapter Seven Orthogonality in Vector Spaces
7.1 Scalar Products in Euclidean Space 193
7.2 Inner Product Spaces 209
7.3 Orthonormal Sets and the Gram-Schmidt
Process 226
7.4 The Method of Least Squares 241
Chapter Eight Eigenvectors and Eigenvalues
8.1 Basic Theory of Eigenvectors and Eigenvalues 257
8.2 Applications to Systems of Linear Recurrences 276
8.3 Applications to Systems of Linear Differential
Equations 288
