SPECIFIC LEARNING GOALS:
The aim of this course is to carry out an introduction to Linear Algebra. More precisely, at the end of the term, the students must be able to
1. Solve and discuss systems of linear equations by Gaussian elimination.
2. Manipulate matrices and vectors (addition; multiplication, computation of inverse matrices and determinants whenever is possible).
3. Decide if a family of vectors are linearly dependent or independent.
4. Determine if a family of vectors spans a vector subspace. If so, find one of its basis.
5. Determine if a transformation is linear or not. If so, rewrite such a transformation in terms of matrices in different basis.
6. Determine if an endomorphism can be diagoanlized or not. Diagonalize endomorphisms whenever is possible.
7. Manipulate the abstract notions of scalar product and norm.
8. Obtain an orthonormal basis from a non-orthogonal basis by means of Gram-Schmidt method.
9. State and solve linear model problems by means of least square problems. Solve such problems with orthogonal projections.
10. Obtain singular value decomposition and Moore-Penrose inverse of matrices.
11. State and solve linear model problems by means of least square problems. Solve such problems with singular value decomposition.
OTHER LEARNING GOALS:
1. Develop the ability to analize and summarize.
2. Model and solve problems.
3. Express mathematical reasoning in oral and written form.