I wonder what does the \(l_\infty\) is. I don't remember seeing it somewhere else. I tried to find help on the internet, but it was always related to highly complex mathematical concepts and I was not able to understan what it does :(
Maybe the definition of the \(l_\infty\)-norm seems complex on internet but it is very simple to understand. This is the maximum of the absolute value of the coefficient of your vector.
As a reminder for \(x\in\mathbb R^d\) :
$$ \| x\|_\infty = \max_{1\leq i \leq d} |x_i| $$
$$ \| x\|_2 =\sqrt{ \sum_{i=1}^d x_i^2}$$
$$ \| x\|_1 =\sum_{i=1}^d |x_i|$$
And more generally:
$$ \| x\|_p =(\sum_{i=1}^d |x_i|^p)^{1/p}$$
Therefore you see that the \(l_\infty\)-norm is the limit of the \(l_p\)-norm for p going to \(\infty\).
l infinity norm
Good evening,
I wonder what does the \(l_\infty\) is. I don't remember seeing it somewhere else. I tried to find help on the internet, but it was always related to highly complex mathematical concepts and I was not able to understan what it does :(
Hi,
Maybe the definition of the \(l_\infty\)-norm seems complex on internet but it is very simple to understand. This is the maximum of the absolute value of the coefficient of your vector.
As a reminder for \(x\in\mathbb R^d\) :
$$ \| x\|_\infty = \max_{1\leq i \leq d} |x_i| $$
$$ \| x\|_2 =\sqrt{ \sum_{i=1}^d x_i^2}$$
$$ \| x\|_1 =\sum_{i=1}^d |x_i|$$
And more generally:
$$ \| x\|_p =(\sum_{i=1}^d |x_i|^p)^{1/p}$$
Therefore you see that the \(l_\infty\)-norm is the limit of the \(l_p\)-norm for p going to \(\infty\).
Best,
Nicolas
4
Alright, thanks a lot for your answer :)
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