Talk:Character (mathematics)
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Finiteness in the Definition of the Character of a Representation edit
In the section of characters of representations, the definition of the character is given in terms of the trace of the representation. The conventional definition of the trace of a linear transformation f on a vector space V (and the one currently provided on the trace page) gives Tr(f) as the sum of the diagonal entries in the matrix representation [f] of f with respect to a basis for V. This definition is not well-defined for infinite-dimensional V, so I've gone ahead and corrected the definition of a character here to reflect that.
Also, the current citation of Serre's text on linear representations of finite groups only provides a definition for the character of a representation of a finite group G. As such, I've removed the citation, since the definition provided does not depend on the cardinality of G. -mathemajor (talk) 02:40, 19 November 2010 (UTC)
- In general, when modifying the definition, you should also provide a new citation rather than just deleting the old one. I put the old one back in for now. Sławomir Biały (talk) 19:14, 8 May 2012 (UTC)
Harmonics edit
It is unclear to me what "If is a finite abelian group, the characters play the role of harmonics." This should be expanded or include a link to some page (harmonics?) that explains what this is. — Preceding unsigned comment added by Abenthy (talk • contribs) 2021-07-20T16:00:09 (UTC)