Guia docente 2023_24 Escuela Superior de Ingeniería Informática

Contents

Topic	Sub-topic
BLOCK I	SYSTEMS OF LINEAR EQUATIONS: Elementary row operations. Echelon form and Reduced Echelon Form. Vector equations. Matrix equations and homogeneous systems. LINEAR MAPS Linear independence and linear maps. The questions of existence and uniqueness in terms of linear maps. MATRICES: Matrix product. LU factorisation. Invertible matrices. Partitioned matrices. Subspaces and basis. Dimension and Rank. .
BLOCK II	DETERMINANTS: Definition of determinants and cofactors. Calculation by elementary operations. Applications of determinants. VECTOR SPACES: Definition and examples of vector space. Coordinates. Vector subspaces. Linear maps and their associated subspaces. The matrix of a linear map and change os basis. Similar matrices. DIAGONALIZATION: Eigenvectors and eigenvalues. Eigenspace of an eigenvalue. Characteristic polynomial. Diagonalizable matrices and applications. .
BLOCK III	ORTHOGONALITY AND LEAST SQUARES: Inner product spaces and orthogonality. Orthogonal projection on a subspace. Gram-Schmidt algorithm and QR decomposition. Least Squares problems. SYMMETRIC MATRICES AND QUADRATIC FORMS: Orthogonal diagonalization of symmetric matrices. Quadratic forms. .
LABORATORY PRACTICES	- Systems of linear equations. - Matrix calculations. - Geometric applications in the plane and in space. - Matrix diagonalization. - Inner product spaces. - Classification of quadratic forms.