A matrix theory of n-dimensional mathematical field and the motion of mathematical points in n-dimensional metric space is developed. Two spaces are considered: the n-dimensional space of an integrable coordinate vector {x} with the integrable metric g(x) and the n-dimensional space of a non-integrable but differentiable coordinate vector {Q}, where dQ = edx, dT(2) = d (Q) over tilde dQ = d (x) over tildeg(x) dx, g(x) = (e) over tildee, partial derivative(Q) = e(-1)partial derivative(x). We call the coordinate space of the vector {Q} as the absolute space. The derivatives of the non-integrable but differentiable matrix eare expressed through the elements of the Christoffel symbols and the elements of the Ricci and Riemann curvature matrices. The absolute velocity vector u(Q) = dQ/ dT and the absolute mathematical field matrix P = u(Q)(partial derivative) over tilde (Q) are introduced. We obtain two groups of the matrix field equations, the first of which is written in the two following forms:partial derivative(Q) < P > - (P) over tilde partial derivative(Q) =rho u(Q), Ku(Q) =rho u(Q), where < P > the trace of the matrix P, K is is the absolute Ricci matrix function, u (Q) is the n-dimensional absolute velocity vector, rho is a scalar function, which is the eigenvalue of K with the corresponding eigenvector u (Q). The interpretation of this pure mathematical theory in 4-dimensional space is the theory of the electromagnetic and gravitational fields and the motion of charged and neutral particles in the electromagnetic-gravitational field.
