# Character of direct sum of linear representations is sum of characters

From Groupprops

## Statement

Suppose is a group, is a field, and are finite-dimensional linear representations of over . Denote by the characters of the representations respectively. Denote by the direct sum of linear representations and by its character. Then, we have the following for any :

Recall that the character of a linear representation is the function that sends any to the trace of the corresponding linear map.