L^p-norms are some functions which takes a vector as input and output a value. It is written as \left\|\mathbf x\right\|_ p.
It is a measure of how many non-zero values are there in the vector. If have to put it into notations, we need to first define 0^0=0. The the L^0-norm is as follows.
We also use its squared form quite often.
For 0< p< \infty, we have the following general form.
Following is a visualization of the contour line of different p values with the norm value equal to 1.