| Code |
15068
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| Year |
1
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| Semester |
S1
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| ECTS Credits |
6
|
| Workload |
TP(60H)
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| Scientific area |
Mathematics
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Entry requirements |
Mathematics 12(A)
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Learning outcomes |
After successfully completing the course, students will have developed the following skills:
(a) perform operations with matrices and solve systems of linear equations;
(b) calculate determinants and use them to solve problems;
(c) understand vector spaces and subspaces, linear combinations and generating sets, linear dependence and linear independence, basis and dimension of a vector space;
(d) define linear transformations and determine the matrix of a linear transformation;
(e) calculate eigenvalues and eigenvectors of a given matrix and diagonalize a matrix (if possible);
(f) determine change of base matrix and solve related problems;
(g) interpret and solve problems related to the dot product, norm, vector product and mixed product of vectors,
orthogonalization.
(h) use the concepts learned in this course unit to solve problems.
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Syllabus |
1. Matrices and Systems of Linear Equations
Types of matrices; matrix and vector operations; elementary operations and Gaussian elimination; Gauss and Gauss-Jordan elimination methods for solving systems of linear equations; inverse matrices
2. Determinants
Definition and properties; adjoint matrix and inverse matrix, applications.
3. Vector Spaces
Vector space and vector subspace, linear combinations and generating sets, linear dependence and linear independence, basis and dimension of a vector space.
4. Linear Transformations
Definition and properties, matrix of a linear transformation,change of basis matrix.
5. Eigenvalues and Eigenvectors
Eigenvalues and eigenvectors of a matrix,matrix diagonalization.
6. Inner Product Spaces
Inner products, norm, projection,orthonormal bases; Gram-Schmidt orthogonalization process, orthogonal complement of subspace. Vector product,mixed product; geometric applications in R3
7. Normed spaces
Vector and matrix norms
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Main Bibliography |
- Isabel Cabral, Cecília Perdigão, Carlos Saiago, Álgebra Linear, Escolar Editora, 2009
- Luís T. Magalhães, Álgebra Linear como introdução à Matemática Aplicada, Escolar Editora, 2001
- David C. Lay, Linear Algebra and its applications, 5th edition, Pearson, 2016
- Gilbert Strang, Linear Algebra and its applications, 4th edition, Brooks Cole, 2005
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Language |
Portuguese. Tutorial support is available in English.
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