We have a norm on $\mathbb{R}^3$ defined by $\vert (u,v,w)\vert=\max\{|u|,|v|+|w|\}$.

This is vector norm on $\mathbb{R}^3$.

What would be the corresponding $\text{matrix norm}$ on $\mathbb{R}^3$ ?

For example $l_1$ vector norm is given by $|x|=\sum_{i=1}^{3}|x_i|$ and the corresponding matrix norm of a matrix $A=[a_{ij}]_{3 \times 3} \ $ is $|A|=\max_{1 \leq j \leq 3} \sum_{i=1}^{3}|a_{ij}|$.


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