19.2.1.1 Properties of normed spaces

Problem: Let \( X \) be an \( \mathrm{n} \)-dimensional space. Is \( \left|x_{1}\right|+\left|x_{2}\right|+\cdots+\left|x_{n}\right|\left(x=\left(x_{1}, \ldots, x_{n}\right) \in X\right) \) a norm on \( X \) ?