Marlos Viana
University of Illinois at Chicago
Symmetry Studies
Abstract
In this seminar I will outline the theory and methods of symmetry studies,
including the notions of structured data and data reduction by
symmetrically equivalent components. I will briefly review the elements of
linear representation of finite groups and show their relation to
Fisher-Cochran's theory of probability distributions for quadratic forms-
This is the Canonical Decomposition theorem. This relationship will be
introduced within the context of simplifying a simple data structure used
in molecular biology. I will also briefly touch on the techniques of
spectral analysis for data indexed by a finite group and on data
structures induced by point groups from classical chemistry.
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