  During the last century the tensor theory of the gravitational field was
developed. We propose and develop the novel, pure mathematical, matrix theory
of the field in n-dimensional metric space. The definition of the mathematical
field matrix and the equations of motion of the mathematical point are given.
The interpretation of the nature of the mathematical field and the mathematical
points can be different and depends on our knowledge of the nature. It is shown
that the equations of motion are different for symmetric and antisymmetric
field matrices. In the matrix field theory the equations of the field are
rigorously derived. This theory reveals that in the 4-dimensional metric space
the field matrix is the electromagnetic-gravitational field matrix, where the
antisymmetric part is the matrix of electromagnetic field and the symmetric
part is the gravitational field matrix. The partial cases of this matrix are
electric-gravitational, magnetic-gravitational and gravitational field
matrices. It is shown that the elements of all obtained matrices are the
Christoffel symbols of the first and the second order or their derivatives.
