104019 – Linear Algebra

3.5 lecture hours and 2 tutorial hours per week
Syllabus:
1. Polynomials, Complex numbers and Fields
2. Matrices: Addition, multiplication by a scalar, matrix multiplication, special
types of matrices, row reduction, echelon and cannonical matrices, row
operations and row equivalence
3. Systems of linear equations: Properties and solutions, rank of a matrix
4. Vector Spaces: Subspaces, linear combinations, linear span and linear
dependence
5. Basis and Dimension: Including row and column spaces, coordinate vectors
6. Invertible matrices
7. Determinants: Properties and applications
8. Linear Transformations: Definition, Kernel and Image of a linear
transformation, matrix representation of a linear operator according to a given
basis B, transition matrix, operations between transformations, similarity
between matrices
9. Eigenvalues and Eigenvectors: The conditions for a diagonalizable matrix