Teaching GuideTerm
Higher Technical University College of Civil Engineering
  Home | galego | castellano | english | A A A |  
Grao en Tecnoloxía da Enxeñaría Civil
 Subjects
  Álxebra lineal I
   Contents
Topic Sub-topic
I. Preliminars.
 1. Correspondences and maps.
1.1 Sets, Definition and notation. Operations with sets.
1.2 Correspondences. Maps. Definition, properties and classification.

2. Combinatorics.
2.1. Product rule.
2.2. Variations.
2.3. Permutations.
2.4. Combinations.
II. Matrices and determinants. 1. Matrices.
1.1 Basic definitions.
1.2 Operations with matrices.
1.3 Special matrices.

2. Determinants.
2.1 Preliminars on permutacions.
2.2 Determinant of a square matrix: definition and properties.
2.3. Development of a determinant by adjoints.
2.4. Rank of a matrix.
2.5. Inverse of a matrix.

3. Equivalence and congruence of matrices.
3.1 Elementary transformations.
3.2 Row equivalence of matrices.
3.3 Column equivalence of matrices.
3.4 Matrix equivalence.
3.5 Matrix congruence.

4. Systems of linear equations.
4.1 Cramer's rule.
4.2 Rouche-Frobenius' Theorem.
4.3 Gaussian elimination.
III. Vectorial spaces. 1. Vectorial spaces and subspaces.
1.1 Definition and properties.
1.2 Vectorial subspaces.

2. Spanning systems. Free linear systems. Basis.
2.1 Linear combinations of vectors.
2.2 Linear dependence and indepdence of vectors.
2.3 Basis, dimension and coordinates.
2.4 Rank of a vector set.
2.5 Change of basis.
2.6 Equations of a subspace.
2.7 Dimension formula.

3. Linear maps.
3.1 Definitions and properties.
3.2 Matrix form of a linear map.
3.3 Change of basis.
3.4 Kernel and image of a linear.
3.5 Composition fo homomorphisms.

4. Endomorphisms.
4.1 Introduction.
4.2 Eigen values and eigen vectors.
4.3 Diagonalization by similarity.
4.4 Triangularization by similarity. Jordan form
Universidade da Coruña - Rúa Maestranza 9, 15001 A Coruña - Tel. +34 981 16 70 00  Soporte Guías Docentes