Linear algebra and applications

Basic information

Workload: 

45h

Syllabus: 

Matrices and vectors. Linear systems. Gaussian elimination and LU factorization. Orthogonality: projections, orthogonalization and least squares. Decomposition into singular values. Eigenvalues and eigenvectors. Introduction to numerical analysis: stability and conditioning. Applications: reduction of dimensionality and main components; PageRank algorithm and equivalents.

Bibliography

Mandatory: 

  • Poole, D. (2004). Álgebra Linear. Thomson
  • Lima, E. L. (1996). Álgebra Linear. IMPA.
  • Strang, G. (2006). Linear Algebra and Its Applications. Brooks and Cole.
  • Trefethen, L. N., & Bau, D. (1997). Numerical Linear Algebra. SIAM.