What is the correct name for an n-dimensional array in mathematics? I have seen the following:
Which is the right way?
"Array" is not used much in math, except possibly by some computational math authors. I generally think of that as computer science terminology. I think they also allow for non-number objects to appear as entries (like strings, for example), and some people are uncomfortable calling something with string entries a matrix.
"Array" seems to be used to encompass any sort of list of numbers in one shape or another, usually when you identify an object by numerical components. Vectors, linear transformations and tensors (=multilinear transformations) all have coordinate representations, if you fix a basis.
I'm using "array" in "multidimensional array" because some people have a hard time thinking of a matrix as anything besides a flat object, but you can also say "multidimensional matrix". While matrices have rows and columns, the multidimensional versions can "go in more directions".
A matrix has componets with two indices. If your array has items with three indices, you could make them into a cube-matrix. If it has four indicies on each entry, you could make it into a hypercube-matrix etc.