0
$\begingroup$

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 $|A|=\max_{1 \leq j \leq 3} \sum_{i=1}^{3}|a_{ij}|$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.