Creating a vector field plot

I'm Mathcadless at the moment, so can't say precisely why you're seeing 2 and 3, however ...

F is an example of what is referred to a nested array,  that is,  each of its elements is itself an array. In this particular case,  each element is a vector.  So the expression first gets the contents of F's element (i,j) and then gets element 2 or 3 of the resulting vector.

There is no reason in principle why a nested array's elements themselves could not nested arrays,  and so on.

Stuart

The function V returns a two element vector as a function of x any y (i.e at each coordinate x,y there is a vector, not a scalar, value). So each element of F is a two element vector, in which the first element is the x component of the vector, and the second element is the y component of the vector. As Stuart notes, that means F is a nested array. To create the vector field plot the x components and y components need to be separated into two matrices. So this:

(indices 0 and 1, not 3 and 2, as your show) splits the first and second elements of each vector at coordinate i,j into tow separate matrices.

Edit: Perhaps this will help. This is the top left corner of the matrix F: