Applied Math 511b Notes

Robert M. Corless

Jan 31, 1996

• Administration and announcements
• References for linear algebra
• Summary of relevant linear algebra theory
  • Linear equations and matrices
  • Matrix algebra
  • Determinants
  • Cramer's rule
  • Gaussian elimination as a matrix factorization
  • Eigenvalue problems
  • The Singular Value Decompostion
  • So why give exact rational solutions of linear systems, then?
• Linear Algebra in Scientific Computing
  • Principles of Scientific Computing
  • LAPACK
  • Solving linear systems
  • Solving eigenvalue problems
  • Sparse systems
• Linear Algebra in Symbolic Computing
  • Consequences of exact arithmetic
  • Row Echelon Decomposition
• Maple Implementation
  • Source Code
  • Help File
  • Test File for the Share Library.
• Eigenvalue Problems.
  • Symbolic Computation With Eigenvalues
  • An Example Due to Kenton Yee.
  • Remarks on the Larger Problem
• References
• About this document ...