Abstarct
Given a structure S, any other structure homomorphic to S provides, in principle, a representation of S. Thus when you draw a Venn diagram to depict sets and their union and intersection, you resort to a representation. The given structure in this case is a set of sets under union and intersection, and its Venn diagram a geometrical representation of it. Likewise, when you draw a graph for a real-valued function of a real variable, you provide a representation for a given set of ordered pairs of reals, consisting of a collection of points on a plane referred to a particular pair of coordinates.
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Notes
- 1.
Some authors use the term “stable” instead of “invariant”, as for instance Serre [8].
- 2.
I have followed here the approach given in Serre [8, Section 1.3, pp. 5–7].
- 3.
This version of the lemma is taken from Greub [1, p. 54]. It points to the fact that for the result to hold the two sets of operators need not be groups.
- 4.
Tr(A) denotes the trace of the matrix A.
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Sinha, V.P. (2010). Representations of Finite Groups. In: Symmetries and Groups in Signal Processing. Signals and Communication Technology. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9434-6_5
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