Suppose \\(A\\) is row vector, and \\(B\\) is a column vector, and we wish to form their dot product \\(A \cdot B\\).

Now clearly this will only work if the number of columns in \\(A\\) equals the number of rows in \\(B\\).

And _that_ is the general compatibility requirement for \\(A\\) and \\(B\\), in order for the product of \\(A\\) and \\(B\\) to be defined:

\\[ncols(A) = nrows(B)\\]