Isometry

Let $$V_1$$ and $$V_2$$ be normed spaces and let $$T$$ be an operator $$T:V_1\to V_2$$. Then, $$T$$ is injective if $$T\mathbf{v} = \mathbf{0} \implies \mathbf{v} = \mathbf{0}.$$ The operator $$T$$ is called an isometry if $$||T\mathbf{v}||_{V_2} = ||\mathbf{v}||_{V_1}$$.