Guia docente 2023_24 Escola de Enxeñaría de Telecomunicación

Contents

Topic	Sub-topic
Topic 1. Complex numbers.	Operations with complex numbers. Geometric concepts associated with complex numbers. Euler's formula and its consequences.
Topic 2. Matrices and determinants.	Matrix operations: addition, scalar multiplication and product of matrices. Matrix inverse. Block matrices. Determinants.
Topic 3. Systems of linear equations.	Systems of linear equations. Elementary row operations and Gauss method. Numerical methods for systems of linear equations.
Topic 4. Vector spaces and linear transformations.	Linear independence. Subspaces. Basis. Dimension. Rank of a system of vectors. Introduction to linear transformations. Matrix of a linear transformation.
Topic 5. Matrix diagonalization.	Eigenvalues and eigenvectors. Eigenspace. Matrix diagonalization and diagonalizable matrices.
Topic 6. Orthogonallity.	Real Euclidean inner product. Complex Hermitian inner product. Orthogonallity. Gram-Schmidt. Unitary Diagonalization. Singular value decomposition. Matrix rank reduction. The method of least squares. Quadratic forms.