To show the organization of the course that includes this module, follow this link Course organization
The aim is to introduce the basic facts about Linear Algebra and its applications
* Matrices and linear systems: matrices, matrix operations, linear systems of equations, Gauss elimination, inverse matrices, LU decomposition.
* Vector spaces: definition and examples, subspaces, sets of generators. Linear dependendency and independency, bases, dimension.
* Linear maps and associated matrices: composition of linear maps and matrix multiplication, base change, kernel and image of a linear map, rank of matrices, dimension formula.
* Inner products and orthogonality: inner product between vectors, orthogonal and orthonormal bases, orthogonal projections, Gram-Schmidt algorithm.
* Canonical forms: eigenvalues and eigenvectors, characteristic polynomial, geometric and algebraic multiplicity of eigenvalues, diagonalizability criteria.