In mathematics, what is an $N \times N \times N$ matrix? In mathematics, what is an $N \times N \times N$ matrix? I think this is a tensor but definitions of tensors that I have read are so overly complicated and verbose that I have trouble understanding them.

If you are having trouble with tensors, try this:
Imagine that you want to locate a point in 3-dimensional Cartesian plane. You need (x,y,z) coordinates to locate the point. Now imagine that each of these points has a numerical value. Then this three dimensional plane with these numerical value will constitute a matrix. If the length of x, y and z axes, each is N, then you get $N\times N\times N$ matrix.
