In the context of representation theory, which studies how groups can be represented through matrices and linear transformations, the trivial representation is a fundamental concept. The **trivial representation** of a group \( G \) is the simplest way of mapping elements of \( G \) to linear transformations. In this representation, every element of the group is represented by the identity transformation.
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The trivial representation sends every group element to the identity operator. A one-dimensional constant-coordinate line in a permutation representation is an example: relabelling positions leaves a uniform assignment unchanged. A trivial action on a higher-dimensional vector space has many invariant subspaces and is therefore not an irreducible representation.