Linear Algebra and Analytic Geometry II

Code:

M1036

Acronym:

M1036

Level:

100

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2025/2026 - 2S

Active?	Yes
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	95	Official Study Plan	1	-	9	72	243
L:MA	101	Official Study Plan	1	-	9	72	243

Teaching language

Portuguese

Objectives

To introduce the basic concepts and results associated to matrices diagonalization and its application to geometry.

Learning outcomes and competences

A student is expected to know the concepts and basic results introduced  and to master the associated techniques.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

It is assumed in this course that the student is familiar and is capable of using the basic notions of Linear Algebra given in the previous course Álgebra Linear e Geometria Analítica I.

Program

. Eigenvectors and eigenvalues, diagonalizable matrices.
. Inner product spaces.
. Self-adjoint endomorphisms.
. Linear isometries and orthogonal matrices.
. Symmetrical bilinear forms and quadratic forms.
. Jordan Canonical form.

Mandatory literature

Santana , Ana Paula; Introdução à álgebra linear. ISBN: 978-989-616-372-3
Smith, Larry.; Linear Algebra /. ISBN: 1-4612-7238-6

Complementary Bibliography

António Monteiro; Álgebra linear e geometria analítica. ISBN: 972-8298-66-8
C. H. Edwards, Jr; Elementary linear algebra. ISBN: 0-13-258245-7
Howard Anton; Elementary linear algebra. ISBN: 0-471-66959-8
Larry E. Mansfield; Linear algebra with geometric applications. ISBN: 0-8247-6321-1
Luís T. Magalhães; Algebra linear como introducao a matematica aplicada. 5ª ed. ISBN: 972-47-007-0

Teaching methods and learning activities

The content of the syllabus is presented at the lectures, and proposed exercises are solved by the students at the practical classes.

Software

Wolfram|Alpha: Computational Intelligence

keywords

Physical sciences > Mathematics > Mathematical logic
Physical sciences > Mathematics > Algebra > Set theory
Physical sciences > Mathematics > Number theory

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Exame	60,00
Teste	40,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	171,00
Frequência das aulas	72,00
Total:	243,00

Eligibility for exams

No requirements.

Calculation formula of final grade

In the first call the final score will be the sum of the scores obtained in two assessments.
The first assessment, worth 8 (eight) points, will take place during the semestre, in a date to be anounced. The second assessment, worth 12 (twelve) points will take place during the first call of exams.

In the second call, the final score will be the obtained in an exam, worth 20 (twenty) points. The exam will be divided in two parts, corresponding to the two assessments. All the students who have not been approved in the course, will be given the oportunity of using their score on one of the assessments (in replacement for the resolution of the corresponding part in the exam).

Special assessment (TE, DA, ...)

Any examination required under special statutes will consist of a written exam which may be preceded by a previous oral test. If in the oral test the students shows that he doesn't know enough, the student will be failed and will not be allowed of writting the written examination.

Classification improvement

Exam in the make up period. These students will not the allowed to take part of the continuous assessment of the course.

Observations

Any student can be asked to do an oral examination in case there are some doubts about the written examination. In such a case the final score will be the arithmetic media of the written and the oral examination.