1. Introduction to the complex numbers. Vector spaces, subspaces, linear combinations, span.
2. Matrices: operations, inverses. Gaussian elimination, rank of a matrix.
Gauss-Seidel method for inverting matrices.
3. Linear independence, basis and dimension.
4. Solutions of systems of linear equations and the structure of the solution.
5. Determinants. Eigenvalues and eigenvectors, diagonalization of matrices.
Jordan form.
6. Linear transformations: kernel and image, matrix of a transformation,
changing bases.
7. Inner product spaces, orthogonality, Gram-Schmidt method. Hermitian and unitary matrices. Least squares solutions.
Bibliography:
1. Hoffman and Kunze, ”Linear Algebra”, Prentice-Hall 1971
2. Lifschutz: Linear Algebra (Schaum series)
3. B. Noble and J.W. Daniel, Applied Linear Algebra, Prentice Hall, 1987.
4. G. Strang, Linear algebra and its applications, Brooks Cole, 2005
Evaluation:
Assignments: 20% of final grade.
Final exam: 80% of final grade.