# Definition:Equivalent Linear Representations

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## Definition

Let $ \struct {G, \cdot}$ be a group.

Consider two linear representations $\rho: G \to \GL V$ and $\rho': G \to \GL W$ of $G$.

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

This has to be rewritten.In particular: above line needs rewriting, but I can't come up with a suitable replacementYou can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by doing so.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Rewrite}}` from the code. |

This article, or a section of it, needs explaining.In particular: The "isomorphic" link goes to a generic "abstract algebra" page, but I believe no actual definition has been made for an isomorphism between two G-modules.You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by explaining it.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Explain}}` from the code. |