Consider the vector norm $\|\vec{x}\|=\frac{1}{n}\sum_{j=1}^n|x_j|$, for $\vec{x}\in\mathbb{R}^n$.
I have shown that the matrix norm induced by this vector norm is $\|A\|=\frac{1}{n}max_j\big(\sum_{i=1}^n|A_{ij}|\big)$.
I am looking to show that infinitely many vector norms induce this same matrix norm. I am a bit stumped with this and don't know where to start. My only guess is that it may have something to do with its similarity to the column sum matrix norm.