| 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 |
| Basic bibliography: Jacob, B.: Linear Algebra. W.H. Freeman and Company. Sancho San Román, J.: Algebra Lineal y Geometría. Octavio y Félez. Castellet, M. - Llerena, I.: Algebra Lineal i Geometría. Manuales de la UAB. Complementary bibliography: Jacob, B.: Linear Functions and Matrix Theory. Springer-Verlag. Hungerford, T.W.: Algebra. Springer-Verlag. |
| Continguts |
| The contents are distributed in two parts, one of them is devoted to standard contents of linear algebra and, in the other, the algebraic structures of group and ring are introduced: - Contents on linear algebra: Systems of linear equations over a field. Methods of Gauss and Gauss-Jordan. Matrices over a field. Elemental matrices. The reduced row-equelon form of a matrix. Rank of a matrix. The Rouché-Frobenius theorem. Characterization of invertible matrices. Determinant function. The formula of Laplace. Determinant of a square matrix. Vector spaces. Subspaces and operations with subspaces. Linear dependence. Basis. Dimension. Coordinates. Linear transformations. Kernel and image. Canonical decomposition of a linear transformation. Linear transformations and matrices. Coordinate-change matrix. Equivalent matrices. Similar matrices. Dual vector space. Dual basis. Eigenvalues and eigenvectors. Diagonalizable endomorphisms and matrices. - Contents on basic algebraic structures: Groups. Subgroups. Normal subgroups and quotient group. Group homomorphisms. Cyclic groups. Symmetric and alternating groups. Rings. Subrings and ideals. Quotient ring. Ring homomorphisms. Divisibility in integral domains. Quotient field of an integral domain. Polynomials over a ring. The division algorithm. Roots of polynomials. Polynomials over a field: structure and factorization. |
| Objetius |
| The aim of this subject is that students get to know and handle the corresponding topics of the following items: -Introduction to the basic algebraic structures. Vector spaces. Linear transformations. Matrices. Determinants. Systems of linear equations. Eigenvalues and eigenvectors. Diagonalization. |
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