I have read the following sentence in Vinberg "linear representations of groups" pg.58:
"Since isomorphic representations are given in compatible basis by identical matrices, we see that isomorphic representations have equal characters "
But I do not understand the first half (the part before the comma) of the sentence, may be because I have not seen an example of it, could anyone give me an example please?
For the second half I understand it as the characters are the traces of the representations.