  The sets ${\Phi({F}^{\mu \nu})}, {\Phi(\tilde {F}^{\mu \nu})}$ of linear
functionals on the space $< F,+,\cdot >$ represent themself linear space $<
\Phi,+,\cdot >$ over the field of \textit{scalars} $P$, which is dual to space
$< F,+,\cdot >$, but it is substantial, that given linear space is not
self-dual. It has been found, that the partition of linear space $< F,+,\cdot
>$ over the field of genuine scalars and pseudoscalars, the vectors in which
are sets of contravariant and covariant electromagnetic field tensors and
pseudotensors ${{F}^{\mu\nu}}$, ${\tilde{F}^{\mu\nu}}$, ${{F}_{\mu\nu}}$,
${\tilde{F}_{\mu\nu}}$, on 4 subspaces takes place. It corresponds to
appearance of 4 kinds of electromagnetic field potential 4-vectors $A_{\mu}$,
which are transformed according to the representations of general Lorentz group
with various symmetry relatively improper rotations. It has been found, that
conserving quantity, corresponding to complex fields is complex charge. It is
argued, that electromagnetic field in the matter is complex field and that
two-parametric group $\Gamma(\alpha,\beta) = U_{1}(\alpha) \otimes \mathfrak
R(\beta)$, where $\mathfrak R(\beta)$ is abelian multiplicative group of real
numbers (excluding zero), determines the gauge symmetry of electromagnetic
field. It is also argued, that free electromagnetic field is characterized by
pure imagine charge.
