Linear Algebra -

1.  Vector spaces, subspaces, linear dependence, basis, dimension, algebra of linear transformations. 
2. Algebra of matrices, rank and determinant of matrices, linear equations. 
3. Eigenvalues and eigenvectors, Cayley-Hamilton theorem. 
4. Matrix representation of linear transformations. Change of basis, canonical forms, diagonal forms, triangular forms, Jordan forms. 
5. Inner product spaces, orthonormal basis. 
6. Quadratic forms, reduction and classification of quadratic forms