I'm trying to find a way describe in mathematical terms a function that takes one or more inputs but the input and output of the function have the same dimensions or shape.
Let's say $x$ is a vector of length $n$. $y$ is also a vector of length $n$ is there a term that describes a function $f$ where $f(x,y) = z$ and $z$ has the same length as $x$ and $y$. The terms isomorphism and homomorphism have been thrown around but I feel like either these terms are not narrow enough or they are too complicated to understand in this simple case.
Essentially I'm looking for a term (and maybe a branch) that describes relations of this type, the shape of the input matches the shape of the output. And if there is a term that describes the opposite where the shape of the output does not match the shape of the input that would be helpful too!