Talk:Character (mathematics)

Finiteness in the Definition of the Character of a Representation

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)[reply]

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)[reply]

Harmonics

It is unclear to me what "If $G$ 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)