i cant understand this definition
norm describes the length of a vector
so if x is our vector
what do we sum in the formula?
why there is absolute value in a vector?
what is x_i?
1) Take the absolute value of each of them.
2) Take the power of each.
3) Sum them all.
4) Take the root of that sum.
For example, if p= 1, that is just the sum of the absolute values.
If p= 2, it is just the usual "Euclidean" norm on .
If p= 3 , n= 4, , , , and , the norm is .
If p= 2 or any even power, you don't need the absolute value. But with odd p, odd powers could cancel- and we don't want that. (1, -1) is not the 0 vector so it shouldn't have 0 norm. But if we used p= 3 without the absolute value, we would have . With the absolute value that becomes