Norms of a vector: maxnorm l1norm l2norm norm

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

There are different norms for vectors in ℝn, and Xcas has different commands for them.

Given a list L=[a1,…,an],

- maxnorm(L) returns the l∞ norm of L, namely max(|a1|,|a2|,…,|an|)

  #### Example.

  Input:

  maxnorm([3,-4,2])

  Output:

  4

  Indeed, 4=max(|3|,|−4|,|2|).

- l1norm(L) returns the l1 norm of L, namely |a1|+|a2|+⋯+|an|. coordinates.

  #### Example.

  Input:

  l1norm([3,-4,2])

  Output:

  9

  Indeed, 9=|3|+|−4|+|2|.

- norm(L) or l2norm(L) returns the ℓ2 norm of L; namely √|a1|2+|a2|2+⋯+|an|2.

  #### Example.

  Input:

  norm([3,-4,2])

  Output:

  √ |
  29

  Indeed, 29=|3|2+|−4|2+|2|2.