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For questions about the algebraic concept of 'character': a function from a group into a field satisfying certain properties. Not to be confused with the more commonly known psychological term.

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"Simple" proof of irreducible characters of finite groups being non-zero

I am wondering, is there a simpler proof (or a proof requiring only materials covered in a standard representation theory course) of characters being non-zero, if I only care about about irreducible characters