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During the last century the tensor theory of the gravitational field wasdeveloped. We propose and develop the novel, pure mathematical, matrix theoryof the field in n-dimensional metric space. The definition of the mathematicalfield matrix and the equations of motion of the mathematical point are given.The interpretation of the nature of the mathematical field and the mathematicalpoints can be different and depends on our knowledge of the nature. It is shownthat the equations of motion are different for symmetric and antisymmetricfield matrices. In the matrix field theory the equations of the field arerigorously derived. This theory reveals that in the 4-dimensional metric spacethe field matrix is the electromagnetic-gravitational field matrix, where theantisymmetric part is the matrix of electromagnetic field and the symmetricpart is the gravitational field matrix. The partial cases of this matrix areelectric-gravitational, magnetic-gravitational and gravitational fieldmatrices. It is shown that the elements of all obtained matrices are theChristoffel symbols of the first and the second order or their derivatives.

Mathematical matrix theory of the field in n-dimensional metric space:  rigorous derivation of the equations of the field with application in  electromagnetic-gravitational fields