Pointwise - Componentwise Operations

Componentwise Operations

Componentwise operations are usually defined on vectors, where vectors are elements of the set for some natural number and some field . can be generalized to a set. If we denote the -th component of any vector as, then componentwise addition is .

A tuple can be regarded as a function, and a vector is a tuple. Therefore any vector corresponds to the function such that, and any componentwise operation on vectors is the pointwise operation on functions corresponding to those vectors.