Definition:Faithful Linear Representation of Group

Definition

Let $ \struct {K, +, \circ}$ be a field.

Let $V$ be a vector space over $K$ of finite dimension.

Let $\GL V$ be the general linear group of $V$.

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

Let $\rho : G \to \GL V$ be a linear representation of $G$ on $V$.

Then $\rho$ is faithful if and only if the kernel of $\rho$ is trivial.

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