  Spontaneous mirror symmetry violation is carried out in nature as the
transition between the usual left (right)-handed and the mirror right
(left)-handed spaces, in each of which the usual and mirror particles have the
different lifetimes. As a consequence, all equations of motion in a unified
field theory of elementary particles include the mass, energy and momentum as
the matrices expressing the ideas of the left- and right-handed neutrinos are
of long- and short-lived objects, respectively. These ideas require in
principle to go away from the chiral definitions of the structure of matter
fields taking into account that the internally disclosed Dirac matrices are, in
the Weyl presentation, reduced to the matrices having an internal undisclosure.
We discuss a theory in which a set comes forward at the new level, namely, at
the level of set-matrix duality principle as a criterion for matrices. This
connection gives the exact mathematical definitions of internally disclosed and
undisclosed matrices, allowing to formulate four more definitions, three lemmas
and one pair of axioms. Thereby, it involves that there is no single matrix,
for which an absolutely empty matrix would not exist. The sets of matrix
elements and the matrices of set elements thus found unite all of matrix and
set operations necessary for deciding the problems in a unified whole.

General Physics