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.
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. Eigenvector sand eigen values. Algebraic and geometric multiplicity of an eigenvalue. Jordan canonical form. Applications (e.g. systems of linearordinary differential equations with constant coefficients, stability of linear dynamical systems, Markov chains, PageRankalgorithm).
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.
The teaching methodologies aim to promote learning based on problem solving and projects, reinforcing the practical component, active learning, autonomous work and student accountability. The assessment model incorporates exam/tests, possibly with minimum grade, complemented with continuous evaluation components and oral evaluation for grades above 17 (out of 20).
* Linear Algebra and its applications, D. Lay, S. Lay, and J. McDonald, 2016, (5th edition), Pearson Education.;
* Linear Algebra, J. Hefferon, 2017, (3rd edition), Saint Michael's College;
* Álgebra Linear como Introdução à Matemática Aplicada, L. Magalhães, 1998, (8ª edição), Texto Editora;
* Introduction to Linear Algebra, G. Strang, 2016, (5th edition), Wellesley-Cambridge Press,
* Linear Algebra, S. Friedberg, A. Insel and L. Spence, 2003, (4th edition), Pearson Education.
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