Prerequisites: Linear Algebra (undergraduate) and Line Analysis (undergraduate).

Fundamentals of matrix algebra: Elementary operations and solution of linear systems: ill-conditioned problems. Linear spaces: the four linear spaces associated with a matrix; linear applications: changes of basis. Spectral theory: determinants, eigenvalues/autovectors; normed spaces; orthogonal and oblique projections; least squares and other minimization methods; positive definite matrices (self-adjoint applications). Matrix calculus: differentiation rules and matrix functions (exponential of a matrix). Applications in modeling and numerical analysis.

References:
LAX, P. – Linear Algebra, New York. John Wiley, 1997.
LIMA, E. L. – Linear Algebra. Coleção Matemática Universitária, IMPA, 1995.
STRANG, G. – Linear Algebra and its Applications. 3 ed. San Diego. HBJ, 1988.

* Basic syllabus. The teacher has the autonomy to make any changes.