Linear Algebra and Analytic Geometry II
| Code: | M1036 | Acronym: | M1036 | Level: | 100 |
| Keywords | |
|---|---|
| Classification | Keyword |
| OFICIAL | Mathematics |
Instance: 2022/2023 - 2S 
| Active? | Yes |
| Web Page: | https://moodle.up.pt/course/view.php?id=1037 |
| Responsible unit: | Department of Mathematics |
| Course/CS Responsible: | Bachelor in Mathematics |
Cycles of Study/Courses
| Acronym | No. of Students | Study Plan | Curricular Years | Credits UCN | Credits ECTS | Contact hours | Total Time |
|---|---|---|---|---|---|---|---|
| L:M | 99 | Official Study Plan | 1 | - | 9 | 84 | 243 |
| L:MA | 39 | Official Study Plan | 1 | - | 9 | 84 | 243 |
Fields changed: Program, Fórmula de cálculo da classificação final
Teaching language
PortugueseObjectives
To learn several basic concepts of Linear Algebra.Learning outcomes and competences
To understand and to be able to use the concepts and the results that were taught.Working method
PresencialPre-requirements (prior knowledge) and co-requirements (common knowledge)
Basic concepts introduced at the unity Linear Algebra and Analytic Geometry I.Program
- Eigenvectors and eigenvalues of an endomorphism and a matrix; algebraic and geometric multiplicity of eigenvalues; endomorphisms and diagonalizable matrices; eigenspaces and generalized eigenspaces; minimal polynomial of an endomorphism; decomposition of a complex vector space as a direct sum of the generalized eigenspaces of an endomorphism; Hamilton-Cayley theorem; nilpotent endomorphisms and their characterization; Jordan's canonical form in the complex case, and determination of a basis for which the endomorphism matrix is in canonical form; brief reference to Jordan's canonical form in the real case.
- Linear isometries and orthogonal matrices; geometric characterization of linear isometries in R^2 and R^3; reference to non-linear isometries (any isometry is composed of a translation with a linear isometry); GL(n), SL(n), O(n), SO(n) groups.
- Symmetrical bilinear forms; adjoint of an endomorphism and self-adjoint endomorphisms; spectral theorem; diagonalization of symmetric bilinear forms and quadratic forms; study of conics and quadrics.
Mandatory literature
Luís T. Magalhães; Algebra linear como introducao a matematica aplicada. 5ª ed. ISBN: 972-47-007-0Howard Anton; Elementary linear algebra. ISBN: 0-471-66959-8
Complementary Bibliography
Morris W. Hirsch; Differential equations, dynamical systems, and linear algebra. ISBN: 0-12-349550António Monteiro; Álgebra linear e geometria analítica. ISBN: 972-8298-66-8
Teaching methods and learning activities
Lectures and classes: the contents of the syllabus are presented in the lectures, where examples are given to illustrate the concepts. There are also practical lessons, where exercises and related problems are solved. All resources are available for students at the unit’s web page.Software
Wolfram|Alpha: Computational IntelligenceEvaluation Type
Distributed evaluation without final examAssessment Components
| designation | Weight (%) |
|---|---|
| Teste | 100,00 |
| Total: | 100,00 |
Amount of time allocated to each course unit
| designation | Time (hours) |
|---|---|
| Estudo autónomo | 159,00 |
| Frequência das aulas | 84,00 |
| Total: | 243,00 |
Eligibility for exams
No requirements.Calculation formula of final grade
- April, 13, 2023;
- May, 30, 2023.
The final score will be the sum of the two test scores.
All registered students are admitted, without restrictions, to the tests and exams.
Special assessment (TE, DA, ...)
Classification improvement
The general evaluation rules apply.
Observations
Docenteapdias(at)fc.up.pt
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