| Center |
| Faculty of Mathematics |
| Departament |
| Algebra |
| Lecturers in charge |
| Sin datos cargados |
| Met. Docent |
| In the theoretical sessions, the active part of its development will correspond basically to the professor. The participation and work of the students in the classroom will be promoted, specially in the practical sessions. |
| Met. Avaluació |
| A theoretic and practical examination will be made. In the final qualification, may also be valued the resolution of questions, problems and exposition of subjects that colud possibly be proposed. |
| Bibliografia |
| T.W. Hungerford. Algebra, Springer, 1974 B.Jacob. Linear Algebra. Freeman and Company, 1990 N.Jacobson. Lectures in Abstract Algebra II, Freeman and Company, 1985. J.Sancho San Román. Algebra Lineal y Geometría, Octavio y Felez, 1976 K. Spindler. Abstract Algebra with Applications. (V.I), Marcel Dekker, 1994. |
| Continguts |
| Matrix polynomials: equivalence, characterizations. Hamilton-Cayley theorem. Frobenius theorem. Canonical forms of an endomorphism h of a finite-dimensional vector space V. Decomposition theorems of V as direct sum of h-invariant subspaces. Bilinear forms. Congruence between real symmetric matrix. Euclidean spaces. Schmidt's orthonormalization method. Orthogonal matrix. Orthogonal congruence between real symmetric matrix. Classification of isometries. Introduction to tensorial algebra: p-covariant tensors, symmetric and antisymmetric tensors, exterior product. |
| Objetius |
| 1) To obtain canonical forms of an endomorphism h of a finite-dimensional vector space V. To obtain decomposition theorems of V as direct sum of cyclic subspaces, 2) To study euclidean spaces: i) simultaneous diagonalization, ii) characterization of the congruence (orthogonal congruence) between real symmetric matrix, iii) characterization of conjugacy classes of the orthogonal group. 3) To introduce tensorial algebra. |
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