Class Algebra

Provides a wide range of basic mathematical knowledge, skills and tools essential for Engineering studies.

Properties of real numbers and complex numbers. Types of matrices. Matrix operations. Matrix algebra. Transposed, symmetrical, and hemi-symmetrical.

Systems of linear equations. Gauss elimination. Linear independence. Rank. Invertible matrices.

Determinants. Laplace's theorem. Cramer's Rule.

Eigenvectors and eigenvalues.

Vector spaces. Subspaces. Base and dimension.

Linear transformations. Injective and surjective transformations. Image and kernel. Matrix of a linear transformation. Vector spaces with internal product.

Series of exercises will be proposed with the aim of consolidating knowledge and stimulating problem-solving skills. The evaluation of the discipline, expressed on a scale from 0 to 20 points, will be made at different times, including 2 midterms (40% + 50%) and individual work to be developed outside the classroom (10%). If the weighted average of these evaluations is equal to or greater than 9.5, the student will be successful in the subject, otherwise the student will be able to attend a global frequency. In the final exam, the student can improve the grade. The minimum passing grade for these assessments is also 9.5. Assessment criteria are explained at the beginning of the semester.

Cabral, I., Perdigão, C., Saiago, C. - Álgebra Linear., 5ª ed., Lisboa: Escolar Editora, 2018  

Strang, G. - Linear Algebra,  5ª ed.,  MA: Wellesley-Cambridge Press, 2016