  We investigate the theoretical impedance equations for several near-field
antenna positions. In the standard model one computes the currents at the
antennas for given voltages using the impedance matrix of the antennas, which
is only possible if the determinant of the impedance matrix is non-zero. We
consider Hertzian group antennas, its relative corresponding impedance and two
approximations (mid and far) of it. For the approximations we show that for
many situations the determinant is zero.
  We find three antenna configurations for three antennas, i.e., on a line, on
a right triangle, and an isosceles triangle, which result in a zero determinant
of the impedance for the far-field approximation. This means that with existing
methods, one cannot determine the behavior of this antenna system. For the
better mid approximation, we find a configuration of 15 triangular-positioned
antennas resulting in a singular impedance matrix.
  Furthermore, we investigate $n\times n$ grid placed antennas in the more
accurate Hertzian impedance model and find that for $d \approx 0.65$
wavelengths of grid distance for n = 2, ..., 8 the absolute value of the
determinant of the corresponding impedance matrix decreases by an order of
magnitude with each increased grid size.
