14.1.1  Norms of a vector

There are different norms for vectors in ℝⁿ, and Xcas has different commands for computing them. Let L=[a₁,…,a_n] be a list.

maxnorm(L) returns the ℓ^∞ norm of L, namely max{|a₁|,|a₂|,…,|a_n|}. For example:

Indeed, 4=max{|3|,|−4|,|2|}.

l1norm(L) returns the ℓ¹ norm of L, namely |a₁|+|a₂|+⋯+|a_n|. For example:

Indeed, 9=|3|+|−4|+|2|.

norm(L) and l2norm(L) both return the ℓ² norm of L, namely √|a₁|²+|a₂|²+⋯+|a_n|². For example:

Indeed, 29=|3|²+|−4|²+|2|².