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.
Read more about this topic: Pointwise
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