Analytical aspects of computational linear algebra

摘要

This paper deals with a system of ordinary differential equations with known initial conditions associated with a given square matrix. By using standard analytical and computational methods many of the important aspects of the given matrix can be determined. Among these are its determinant, its adjoint, its inverse (if it exist), the coefficients of the characteristic polynomial, the location of the roots ofthe characteristic polynomial, and the corresponding eigenvectors. Concomitently, the differential system yields a treatment of inhomogeneous linear algebraic systems associated with the given matrix, as in economic input-output analysis. In particular, new insights are provided into Faddeev's algorithm for the coefficients of the characteristic polynomial.