On Wikipedia, we have two topics named "Vector Calculus" and "Matrix Calculus", which made me wonder whether they are two different branches of Mathematics. At the beginning, I assumed that both fields are compatible each other as they have a common ground of Linear Algebra and Calculus, but then I realized that some definitions from Vector Calculus conflict with Matrix Calculus (take the ambiguity over the $\nabla^2$ notation as an example [3], [4]). Although they also matches in some definitions, as the gradient vector, for instance (considering the denominator layout in Matrix Calculus).
Is it correct to say that "Vector Calculus" and "Matrix Calculus" can be considered different branches of Mathematics?
