Linear Algebra and Applications

Prerequisites: Linear Algebra (graduation) and Analysis (graduation).
 
Fundamentals of Matrix Algebra: Elementary operations and linear systems solution: ill-conditioned problems. Linear spaces: the four linear spaces associated with a matrix; linear applications: base changes. Spectral theory: determinants, eigenvalues / eigenvectors; normed spaces; orthogonal and oblique projections; least squares and other minimization methods; positive-definite matrices (self-adjoint applications). Matrix calculus: differentiation 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. – Álgebra Linear. Coleção Matemática Universitária, IMPA, 1995.
STRANG, G. – Linear Algebra and its Applications. 3 ed. San Diego. HBJ, 1988.

* Standard program. The teacher has the autonomy to make any changes.