1. Vectors in R" and C" -- 2. Matrix algebra -- 3. Systems of linear equations -- 4. Square matrices -- 5. Determinants -- 6. Algebraic structures -- 7. Vector spaces and subspaces -- 8. Linear dependence, basis, dimension -- 9. Mappings -- 10. Linear mappings -- 11. Spaces of linear mappings -- 12. matrices and linear mappings -- 13. Change of basis, similarity -- 14. Inner product spaces, orthogonality -- 15. Polynomials over a field -- 16. Eigenvalues and eigenvectors, diagonalization -- 17. Canonical forms -- 18. Linear functionals and the dual space -- 19. Bilinear, quadratic, and hermitian forms -- 20. Linear operators on inner product spaces -- 21. Applications to geometry and calculus

1. Algebras
2. Linear -- Problems
3. exercises
4. etc