Guia docente 2013_14 Escuela de Ingeniería de Telecomunicación

Contents

Topic	Sub-topic
Subject 1. Complex numbers.	Operations with complex numbers. Geometry of the complex plane. Euler's formula and its consequences.
Subject 2. Systems of linear equations.	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.
Subject 3. Vector spaces.	Relations of linear dependence. Subspaces. Basis. Dimension. Rank of a system of vectors. Intersection and sum of subspaces.
Subject 4. Matrices and determinants.	Introduction to linear maps. Matrix of a linear map. Operations with matrices. Inverse matrix. Block matrices. LU decomposition. Determinants. Rank of a matrix.
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. Applications of Linear Algebra.