Dear András,
Try those different option in MATLAB for example. or Octave/Scilab/Sympy-Matrix... they are all the same.
Of course, these are all systems with a focus on matrices per se rather than general arrays. They take liberties with non-2-dim arrays that make sense if the focus is on treating 2-dim arrays as matrices. One of the motivating reason's for numpy's early development (as Numeric) was to get away from those assumptions and limitations and be a general array processing system. Part of the reason that we choose the terminology "multidimensional array" is to emphasize those differences.
The term "multidimensional arrays" is a little bit vague. one might think of multidimensional matrices ( I don't think there is such a thing in math) if coming from MATLAB. I also think the row-major column major terminology is confusing. there are no rows or columns for that matter.
Granted, but it's long-established terminology, and not actually important for a user to know unless if someone is working in C with a flat representation of the allocated memory.
Numpy ndarrays are homogeneous, uniform nested lists. one can represent different layers of this list in different ways using rows or columns.
You have to be careful here as well. "list" also has semantic baggage. Data structures are generally only called "lists" in a wide variety of programming languages if they have cheap appends and other such mutation operations. numpy arrays don't (as well as the things that we call "arrays" in FORTRAN and C/C++ that are distinct from what we would call "lists" in those languages).
Please be assured that "multidimensional array" is terminology that we didn't make up. It does derive from a tradition of mathematical programming in FORTRAN and C and makes meaningful semantic distinctions within that tradition. There are other traditions, and we might well have settled on different terminology if we had derived from those. We do expect people to come from a variety of traditions and have a period of adjustment as they learn some new terminology. That's perfectly reasonable, which is good, because it is entirely unavoidable. There isn't a universal set of terminology that's going to work with everyone's experience out of the gate.
I think the current popular terminology is `tensors` for `multidimensional arrays`. Note that matrices are a different type of object.
Popular, but quite misleading, in the same way that not every 2-dim array is a matrix. As someone who works on tensor machine learning methods once complained to me.