Accession Number:

ADA433787

Title:

Group Theory, Linear Transformations, and Flows: (Some) Dynamical Systems on Manifolds

Descriptive Note:

Briefing charts

Corporate Author:

NORTH CAROLINA UNIV AT CHAPEL HILL

Personal Author(s):

Report Date:

2005-01-03

Pagination or Media Count:

48.0

Abstract:

OUTLINE Motivation Realization process A case study Basic Form Similarity property Decomposition property Reversal property Matrix Groups and Group Actions Tangent Space and Projection Canonical Forms Objective Functions and Dynamical Systems Examples Least squares New Thoughts. CONCLUSION Many operations used to transform matrices can be considered as matrix group actions The view unifies different transformations under the same framework of tracing orbits associated with corresponding group actions It is yet to be determined how a dynamical system should be defined over a group so as to locate the simplest form Continuous realization methods often enable us to tackle existence problems that are seemingly impossible to be solved by conventional discrete methods Group actions together with properly formulated objective functions can offer a channel to tackle various classical or new and challenging problems Some basic ideas and examples have been outlined in this talk New computational techniques for structured dynamical systems on matrix group will further extend and benefit the scope of this interesting topic.

Subject Categories:

  • Numerical Mathematics
  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE