- Fields: definitions, the field of complex numbers.
- Linear equations: elementary operations, row reduction, homogeneous and inhomogeneous systems, representations of the solutions.
- Vector spaces: examples, subspaces, linear dependence, bases, dimension.
- Matrix algebra: matrix addition and multiplication, elemetary operations, the inverse of a matrix, the determinant, Cramer’s rule.
- Linear transformations: examples, kernel and image, matrix representation.
- Diagonalization: eigenvectors and eigenvalues, the characteristic polynomial, applications.
- Bilinear forms.
- Finite dimensional inner product spaces.
- Operators on finite dimensional inner product spaces: the adjoint, self adjoint operators, normal operators, diagonalization of normal operators.