00005 - Algebra

Learning outcomes

By the end of the course, the student is expected to know the basic (elementary) theory of linear algebra, and in particular of matrix algebra. Specifically, the student should be able: to work with finite dimensional vectors and matrices, to solve linear systems, to make orthogonal projections in Euclidean spaces, to diagonalize matrices, and to classify real quadratic forms.

 

 

 

 

 

 

Course contents

Preliminary concepts: Cartesian product. Real numbers. Polynomials and the Fundamental Theorem of Algebra.

Matrices: matrix operations, determinants, invertible matrices.

Linear systems: Gaussian elimination, Cramer’s rule.

Finite-dimensional vector spaces: R^n, vector subspaces, bases, matrix rank, the Rouché–Capelli theorem for systems of linear equations, change-of-basis matrices.

Linear transformations: associated matrix, kernel and image, eigenvalues and eigenvectors, diagonalization, the real spectral theorem.

Bilinear forms and quadratic forms.

Euclidean spaces: inner product, orthogonal bases, orthogonal complement, orthogonal projections.

Readings/Bibliography

Lecture notes provided by the teacher.

The following text-books are suggested for further readings: 

Fioresi R., Morigi M.: Introduzione all'algebra lineare. Seconda edizione, Cea

Schlesinger E.: Algebra Lineare e Geometria, Zanichelli

Teaching methods

Tablet-based lecture notes: the notes produced on the tablet during each lecture are made available on Virtuale.

Each week, two hours of tutorial sessions led by the tutor are scheduled, during which exercises covering all topics in the syllabus are solved.

Assessment methods

The examination consists of a written test with two theory questions and three exercises based on variations of the exercises covered in class. There is no oral examination.

Each theory question is worth 2 points, while the total score for the examination is 33 points.

With regard to assessment, the use of AI is prohibited. Any use of AI constitutes a violation of academic integrity.

Students with specific learning disabilities (SLDs) or temporary or permanent disabilities are advised to contact the relevant University office well in advance (https://site.unibo.it/studenti-con-disabilita-e-dsa/en ). The office will propose appropriate accommodations to the students concerned. These accommodations must, in any case, be submitted to the course instructor for approval at least 15 days in advance. The instructor will assess their suitability, also in relation to the learning objectives of the course.

Teaching tools

Blackboard and Tablet

Office hours

See the website of Sabrina Mulinacci