Matrix Division

Rules are developed for a direct division of matrixes without previous inversion of any factor of the computation. Any nonsingular matrix may be divided by a nonsingular and square matrix, if both matrixes have the same number of rows. The divisor matrix is first factored in a product of two triangular matrixes. The dividend matrix is divided consecutively by the factors of the divisor matrix. In dividing a matrix by a triangular matrix, the elements of the quotient matrix are determined from the multiplication of the rows of the quotient matrix into rows of the divisor matrix, for an orderly generation of the terms of the dividend matrix. One numerical example illustrates the procedure. This division method represents a general form of which Cholesky's scheme is a particular short-cut varient.