The term infinity norm refers to two closely related norms. For a finite vector 
, the infinity norm, also called the maximum
norm, is the L∞-norm
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More generally, the L∞-norm of an essentially bounded measurable function 
is 
, where the abbreviation 
denotes the essential
supremum. The finite-vector formula is the special case for a finite
set with counting measure.
For a matrix, the infinity norm generally means the matrix norm induced by the vector infinity norm. It is the maximum absolute row sum norm,
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In finite-dimensional spaces the vector infinity norm is equivalent to every vector norm, although their numerical values differ.
