For some [[../02 Areas/Math/Linear Transformation|Linear Map]] $T$: If $T:\R^n \to \R^n$ is [[../02 Areas/Math/Injective|one-to-one]], then [[../02 Areas/Math/Universal Quantifier|for any]] $\vec x \neq \vec y \in \R^n \iff T(\vec x) \neq T(\vec y)$. *This is true if and only if:* If $T: \R^n\to \R^n$ is [[../02 Areas/Math/Injective|one-to-one]], then [[../02 Areas/Math/Universal Quantifier|for any]] $\vec x \in \R^n$ , $T(\vec x) \implies \vec x =0$.