Objectives
Master matrix calculus and methods for solving systems of linear equations. Learn about vector spaces and linear transformations. Study canonical forms of matrices, eigenvectors, eigenvalues and singular values. Study applications of the previous subjects.
Program
Gauss and Gauss-Jordan elimination applied to the solution of linear systems. Matrices, inverse matrices and determinants. Definition and examples of vector spaces. Linearly independent sets. Linear transformations. Nullspace (kernel) and range of a linear transformation. Solution space of a linear equation. Eigenvectors and eigenvalues. Algebraic and geometric multiplicity of an eigenvalue. Jordan canonical form. Applications (e.g. systems of linear ordinary differential equations with constant coefficients, stability of linear dynamical systems, Markov chains, PageRank algorithm). Inner product spaces. Gram-Schmidt orthogonalization. The least squares method. Spectral theorem. Orthogonal, unitary and hermitean linear transformations. Singular value decomposition of a linear transformation between euclidean spaces. Classification of quadratic forms.
Evaluation Methodology
Exam/tests, possibly with minimum grade, complemented with continuous evaluation components and oral evaluation for grades above 17 (out of 20).
Cross-Competence Component
The UC allows the development of transversal competences on Critical Thinking, Creativity and Problem Solving Strategies, in class, in autonomous work and in the several evaluation components. The percentage of the final grade associated with these competences should be around 15%.
Laboratorial Component
Not applicable.
Programming and Computing Component
Not applicable.
More information at: https://fenix.tecnico.ulisboa.pt/cursos/lerc/disciplina-curricular/845953938489996
