Definition:Equivalent Representation

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Definition

Let $(G,\cdot)$ be a group.

Consider two representations $\rho: G \to \operatorname{GL} \left({V}\right)$ and $\rho \, ': G \to \operatorname{GL} \left({W}\right)$ of $G$.


Then $\rho$ and $\rho \, '$ are called equivalent (representations) if and only if their correspondent $G$-modules using Correspondence between Linear Group Actions and Linear Representations are isomorphic.