This book provides a complete account of undergraduate linear algebra, in a rigorous style.

1. Matrices; 2. Vector spaces; 3. Inner product spaces; 4. Bilinear and sesquilinear forms; 5. Orthogonal bases; 6. When in a form definite?; 7. Quadratic forms; 8. Linear transformations; 9. Polynomials; 10. Eigenvalues and eigenvectors; 11. The minimum polynomial; 12. Diagonalization; 13. Self-adjoint transformations; 14. The Jordan normal form

Richard KayeLecturer in Pure Mathematics, University of Birmingham, Robert WilsonReader in Group Theory, University of Birmingham