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  "body": "\n## Summary\n\nIn mathematics, especially in an area of abstract algebra known as representation theory, a **faithful representation** ρ of a group $G$ on a [[vector space|000AYPA9AJ]] $V$ is a linear representation in which different elements $g$ of $G$ are represented by distinct linear mappings $\\rho(g)$. In more abstract language, this means that the [[group homomorphism|0HV9Y7WG5R]] $\\rho: G\\to GL(V)$ is injective (or one-to-one).\n",
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