# Monomial linear representation

From Groupprops

*This article describes a property to be evaluated for a linear representation of a group, i.e. a homomorphism from the group to the general linear group of a vector space over a field*

*This article provides a semi-basic definition in the following area:* linear representation theory

## Definition

### Symbol-free definition

A linear representation of a group over a field is said to be monomial if it satisfies the following equivalent conditions:

- It is a direct sum of representations induced from degree-one representations of a subgroup
- We can choose a basis such that every matrix is a monomial matrix with respect to that basis.