1. Linear equations
2. Vector spaces
3. Linear transformation
4. Polynomials
5. Determinants
6. Elementary canonical forms
7. The rational and Jordan forms
8. Inner product spaces
9. Operators on inner product spaces
10. Bilinear forms
Appendix 1. Sets
Appendix 2. Functions
Appendix 3. Equivalence relations
Appendix 4. Quotient spaces
Appendix 5. Equivalence relations in linear algebra
Appendix 6. The axiom of choice
Bibliography
Index