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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“There is a patent office at the seat of government of the universe, whose managers are as much interested in the dispersion of seeds as anybody at Washington can be, and their operations are infinitely more extensive and regular.”
—Henry David Thoreau (1817–1862)