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Linear Algebra and Analytical Geometry

Linear Algebra and Analytical Geometry

Code	11536
Year	1
Semester	S1
ECTS Credits	6
Workload	TP(60H)
Scientific area	Mathematics
Entry requirements	Matemática12(A)
Learning outcomes	This course aims to provide the students with a strong basis of the major tools and methods of an introductory course to Linear Algebra, enhancing its use, either in a pure form or in an applied way, in the future. The syllabus, whose contents are usually taught in similar courses in other European Universities, namely Portuguese, relies on the learning outcomes intended for this curricular unit.
Syllabus	1. Matrices: Types of matrices; Operations with matrices; Rank of a matrix; Inverse of a matrix; Systems of linear equations. 2. Determinants: Determinant of a square matrix; Properties; Cofactors; Laplace’s Theorem; Adjoint matrix and inverse matrix; Application to linear systems of equations; 3. Vector Spaces: Definition of vector space; Subspaces; Linear combinations and spanning set; Linear dependence and independence; Basis and dimension of a vector space; 4. Linear Transformations: Definition and examples; Properties; Matrix of a linear transformation; Change of basis matrix; 5. Eigenvalues and eigenvectors of a matrix: Definition, examples and properties; Similar matrices; Diagonalizable matrices; 6. Inner product spaces: Inner product, Norm; Cauchy–Schwarz inequality; Orthogonality, orthonormal basis and Gram-Schmidt orthogonalization process;
Main Bibliography	Cabral, I., Perdigão, C., & Saiago, C. (2018). Álgebra linear: teoria, exercícios resolvidos e exercícios propostos com soluções, 5º Edição, Escolar Editora. Dias Agudo, F. R. (1996). Introdução à Álgebra Linear e Geometria Analítica. Lisboa: Escolar. Howard, A., & Busby, R. (2006). Álgebra Linear Contemporânea. Porto Alegre: Bookman. Lay, D. C. (2007). Álgebra Linear e as suas aplicações. Rio de Janeiro: LTC. Lipschutz, S. (1972). Álgebra linear: resumo da teoria. São Paulo: McGraw-Hill. Magalhães, L. T. (2001). Álgebra linear como introdução a matemática aplicada. Lisboa: Escolar. Nering, E. D. (1970). Linear Algebra and Matrix Theory. New York: John Wiley. Strang, G. (1976). Linear Algebra and Its Applications. New York: Academic. Vujicic, M. (2007). Linear algebra thoroughly explained. Berlin: Springer Verlag. Rousseau, C., & Saint-Aubin, Y. (2008). Mathematics and technology. New York: Springer.
Language	Portuguese. Tutorial support is available in English.