| Educational guide School of Engineering |
english |
| Degree in Mathematical and Physical Engineering (2021) |
 Subjects |
| LINEAR ALGEBRA |
| Contents |
| IDENTIFYING DATA | 2023_24 |
| Subject | LINEAR ALGEBRA | Code | 17274001 | |||||
| Study programme |
|
Cycle | 1st | |||||
| Descriptors | Credits | Type | Year | Period | ||||
| 7.5 | Basic Course | First | 1Q |
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| Competences | Learning outcomes | Contents |
| Planning | Methodologies | Personalized attention |
| Assessment | Sources of information | Recommendations |
| Topic | Sub-topic |
| 1.-Matrices, Systems of Linear Equations and Determinants | Matrices and vectors: Definitions, Basic Operations and Properties. Linear Combination. Multiplication of Matrices. The 4 spaces of a Matrix. Range inverse matrix Systems of Linear Equations: geometric, vector and matrix views. Gaussian elimination. Determinants: definition and properties. Laplace's rule. Cramer's rule. |
| 2.-Vector spaces |
Definition of the basic Algebraic Structures: Group, Ring, Field. Vector Space: Definition and Examples. Linear Independence. Vector subspace; intersection and addition. Linear span and base. Dimension Grassmann formula. Direct sum. Quotient space. |
| 3.-Linear Maps | Definition, examples and properties. Kernel and Image. Range. Composition of applications. Matrix of an application in some bases. Base change. Isomorphism theorem. Dual space and dual base. |
| 4.-Eigenvalues and Eigenvectors | Definition. Invariant subspace. Characteristic polynomial. Decomposition theorem: diagonalization criteria. Cayley-Hamilton theorem. Minimal Polynomial |
| 5.-Ortogonalization | Dot product. Ortogonality and ortonormal basis. Gram-Schmidt process. Norm, angle and distance. Ortogonal subspaces. Projection onto a subspace. Least squares approximation. |
