TABLE OF CONTENTS
- Systems of Linear Equations
- Vectors
- The Vector Space of m x n Matrices
- Systems of Linear Equations
- Guassian Elimination
- Column Space and Null Space
- Linear Independence and Dimension
- The Test for Linear Independence
- Dimension
- Applications to Systems
- Linear Transformations
- Matrix Transformations
- Matrix Multiplication
- Image of a Transformation
- Inverses
- The LU Factorization
- Orthogonality
- Coordinates in "R"
- Projections: The Gram-Schmidt Process
- Fourier Series: Scalar Product Spaces
- Orthogonal Matrices
- Least Squares
- Determinants
- Determinants
- Determinants and Reduction
- Cramer's Rule and Formula for Inverses
- Diagonalization and Matrix Representation
- Eigenvectors
- The Matrix of a Linear Transformation: Diagonalization
- Complex Eigenvectors
- Orthogonal Diagonalization
- Selected Answers and Hints
- Glossary
- Index
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