Linear Algebra II

Cod: 21003

Department: DCET

Department: DCET

ECTS: 6

Scientific area: Mathematics

Scientific area: Mathematics

Total working hours: 156

Total contact time: 26

Total contact time: 26

Jordan Canonical Form

Inner product

Bilinear forms

Analytic geometry

Inner product

Bilinear forms

Analytic geometry

2. Inner products over a real or complex vectorial space: norms, angles and orthogonality; inequality of Cauchy-Schwarz, triangular inequality and theorem of Pitagoras; orthogonal bases, orthonormal bases and the method of Gram-Schmidt; cross product, triple product; areas and volumes; matrix of an inner product.

3. Bilinear applications and quadratic forms: matrix associated to a quadratic form and its classification.

4. Analytic Geometry: affine space; change of referencial; lines, planes, hyperplanes; vectorial equations, parametric equations, cartesian equations; parallelism, orthogonality; metric problems; conics and quadrics.

[1] CORREIA, Ana Luísa. Álgebra Linear II: support material to be posted in the e-learning platform.

E-learning

Continuous assessment is privileged: 2 or 3 digital written documents (e-folios) during the semester (40%) and a
presence-based final exam (p-folio) in the end of the semester (60%). In due time, students can alternatively choose to perform one
final presence-based exam (100%).

Students are assumed to be conversant with the subject matter studied in *Linear Algebra I.*