### 5.41.1 Norms of a vector : maxnorm l1norm l2norm norm

The instructions to compute the different norm of a vector are :

- maxnorm returns the l∞ norm of a vector, defined as the maximum of the absolute values of its coordinates.
  Input :
  maxnorm([3,-4,2])
  Output :
  4
  Indeed : x=3, y=-4, z=2 and 4=max(|x|,|y|,|z|).
- l1norm returns the l1 norm of a vector defined as the sum of the absolute values of its coordinates.
  Input :
  l1norm([3,-4,2])
  Output :
  9
  Indeed : x=3, y=-4, z=2 and 9=|x|+|y|+|z|.
- norm or l2norm returns the l2 norm of a vector defined as the square root of the sum of the squares of its coordinates.
  Input :
  norm([3,-4,2])
  Output :
  sqrt(29)
  Indeed : x=3, y=-4, z=2 and 29=|x|2+|y|2+|z|2.