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5.2. Linear Algebra (Mandatory)

5.2.1. Justification ↑ Back to top

Linear algebra is a fundamental mathematical tool shared by computer science and engineering disciplines, providing the foundations for structural analysis, circuit networks, control systems, data processing, and algorithm design. This course provides a solid foundation in the concepts and techniques of elementary and advanced linear algebra, with emphasis on its application in scientific and engineering contexts.

5.2.2. Generales Goals ↑ Back to top

1. Understand the fundamental concepts of linear algebra, including vector spaces, linear transformations, and matrix theory.
2. Apply linear algebra techniques to solve systems of equations and eigenvalue/eigenvector problems arising from scientific and engineering contexts.
3. Develop skills in abstract reasoning and logical thinking to address mathematical problems.

5.2.3. Contribution to Outcomes ↑ Back to top

AG-C07) Computing Knowledge: Applies knowledge of mathematics, science, and computing. (Familiarity)

5.2.4. Content ↑ Back to top

5.2.4.1. Linear Algebra (48 hours) [Skills AG-C07] ↑ Back to top

Bibliography: (Strang, 2016; Lay et al., 2016)

Topics

1. Vector spaces and subspaces; bases, dimension, and linear independence
2. Linear maps, kernel and image, rank-nullity theorem, and matrix representations
3. Determinants: definition, properties, Cramer's rule, and geometric interpretation
4. Eigenvalues and eigenvectors; diagonalization and the spectral theorem
5. Inner product spaces, orthogonality, Gram-Schmidt process, and least squares
6. Matrix decompositions: LU, QR, and singular value decomposition (SVD)

Learning Outcomes

1. Identify whether a set with given operations forms a vector space and determine a basis [Familiarity]
2. Compute eigenvalues, eigenvectors, and matrix decompositions to diagonalize or factor matrices [Usage]
3. Apply the SVD and least squares methods to solve overdetermined linear systems and data approximation problems [Assessment]

5.2.5. Bibliography ↑ Back to top

Strang, G. (2016). Introduction to Linear Algebra. Wellesley-Cambridge Press.

Lay, D. C., Lay, S. R., and McDonald, J. J. (2016). Linear Algebra and Its Applications. Pearson.