What is the terminology for vector operations which only require the ith element I have some vector processing code which allows the user to define a left hand side vector terms of the input vectors and scalar constants. The system is aware which parameters are scalars and which are vectors, so the user does not input the indices of the vectors. For example, an equation may look like this: Vout = A*Vin1 + B*Vin2 Where A and B are scalars and Vout, Vin1 and Vin2 are vectors. It is implemented as a very simple loop over the vectors and assumes that the ith element of the left hand side vector is obtained by applying the specified equation to the ith elements of the input vectors. My question is for the purposes of documentation; what is the term for this type of vector operation, i.e. that which only operates on the ith element of every vector?

You are just calculating componentwise.

I would not consider this an operation.

A related operation is called projection onto the $i$-th component. It reduces the vector to its part in $i$-direction. E.g.:

$$ P_1 v = P_1 (x_1 e_1 + x_2 e_2 + x3 e_3) = x_1 e_1 = (v \cdot e_1) \, e_1 $$