Mobilité EUt+
Retour

Page du cours ✏️


Linear Algebra and Analytical Geometry - UTCN
CS2.00

Description
 | Vectors in plane and space.
 | Lines and planes.
 | Vectror spaces: defntion, examles, subsaces, sums of subspaces.
 | Basis and dimensions. Linar indpendence. Change of basis.
 | Inner product spaces (I): definition, examples, computations, orthonormal basis, Schwarz inequalty, orthogonal complement.
 | Inner product spaces (II): Gram-Schmidt ortogonalization process, Gram deteminants. Linear manifolds, distances.
 | Linear maps (I): definition, kernel, image, injective and surjective maps.
 | Linear maps (II): the matrix of a linear map.
 | Eigenvectors and eigenvalues of operators (and associated matrix). Characteristic polynomial. Cayley-Hamilton thoerem. Diagonal form. Diagonaziabel operators.
 | The Jordan canonical form for operators (and associated matrix). Jordan basis, the Jordan matrix.
 | Functions of a matrix. The n-th power of a matrix. Elementary functions of a matrix.
 | The adjoint operator. Definition, properties, examples.
 | Special operators, Properties of eigenvalues and eigenvectors.
 | Bilinear forms, quadratic forms. The associated matrix.
 | Conics and quadrics. Reduction to a canonical form. Geometric properties.

Crédits ECTS
4

Langue d'enseignement
English

Langue d'examen
English

Langue des supports pédagogiques
English

Acquis d'apprentissage fondamentaux

Entité de gestion (faculté)
Automation and Computer Science Faculty - UTCN