Educational guide 2014_15 Escola de Enxeñaría de Telecomunicación

Contents

Topic	Sub-topic
Subject 1. Complex numbers.	Operations with complex numbers. Geometric concepts associated with complex numbers. Euler's formula and its consequences.
Subject 2. Systems of linear equations and matrices.	Solution of a system of linear equations. Systems of linear equations and vector equations. The matrix equation Ax=b. Sets of solutions of systems of linear equations. Operations with matrices. Inverse of a matrix. Block matrices. LU decomposition. Determinants. Rank of a matrix.
Subject 3. Linear transformations	Relations of linear dependence. Subspaces. Basis. Dimension. Rank of a system of vectors. Introduction to linear transformations. Matrix of a linear transformation. Composition of linear transformations.
Subject 5. Eigenvalues and eigenvectors.	Eigenvalues and eigenvectors. Eigenspace. Diagonalizable matrices.
Subject 6. Orthogonallity.	Real Euclidean inner product. Complex Euclidean inner product. Orthogonallity. Diagonalization by unitary similarity. Singular value decomposition. Matrix rank reduction. The method of least squares. Quadratic forms.