| Code |
13899
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| Year |
1
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| Semester |
S1
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| ECTS Credits |
7,5
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| Workload |
TP(75H)
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| Scientific area |
Mathematics
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Entry requirements |
Mathematics of secondary course.
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Learning outcomes |
At the end of this course, students will be able to:
- identify square and rectangular matrices, rows, and columns of a matrix,
- identify diagonal, symmetric, skew-symmetric and hermitian matrices;
- compute the sum, the product and the transpose of a matrix;
- compute the rank of a matrix;
- identify an invertible matrix and compute its inverse;
- solve and classify linear systems of equations;
- compute the determinant of a matrix;
- identify subspaces of a vector space and determine a basis;
- compute the matrix of a linear transformation;
- solve linear systems of equations and compute the inverse of a matrix by using determinants;
- compute the eigenvalues of a matrix and identify diagonalizable matrices;
- compute the inner product, the vector cross product and the scalar triple product of vectors;
- apply the Gram-Schmidt orthogonalization process.
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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 vect or 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;
Ortogonal decomposition;
Vector cross product in R3 and scalar triple product.
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Main Bibliography |
Cabral, I., Perdigão, C., & Saiago, C. (2009). Álgebra linear: teoria, exercícios resolvidos e exercícios propostos com
soluções. Lisboa: Escolar.
Dias Agudo, F. R. (1996). In trodução 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-H ill.
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.
Santana, A. P., & Queiró, J. F. (2010). Introdução à Álgebra Linear. Lisboa: Gradiva.
Cabello, J. (2006). Álgebra lineal: sus aplicaciones en economía, ingenierías y otras ciencias. Madrid: Delta.
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Language |
Portuguese. Tutorial support is available in English.
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