Statements (33)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
mathematical norm
|
| gptkbp:alsoKnownAs |
supremum norm
maximum norm uniform norm |
| gptkbp:appliesTo |
complex vectors
bounded functions real vectors |
| gptkbp:defines |
The L∞ norm of a vector x is the maximum absolute value of its components.
|
| gptkbp:domain |
finite-dimensional vector spaces
space of bounded functions |
| gptkbp:form |
||x||∞ = max_i |x_i|
|
| gptkbp:hasSpecialCase |
Lp norm
|
| https://www.w3.org/2000/01/rdf-schema#label |
L∞ norm
|
| gptkbp:limitation |
Lp norm as p approaches infinity
|
| gptkbp:notation |
L∞
|
| gptkbp:property |
satisfies triangle inequality
is a norm is homogeneous is non-negative is submultiplicative is translation invariant is zero if and only if the vector is zero |
| gptkbp:relatedTo |
gptkb:Lp_space
gptkb:Chebyshev_distance L2 norm supremum norm L1 norm |
| gptkbp:symbol |
||x||∞
|
| gptkbp:usedIn |
functional analysis
linear algebra vector spaces |
| gptkbp:bfsParent |
gptkb:L∞_metric
|
| gptkbp:bfsLayer |
8
|