Control of nonholonomic systems and decomposition of skew symmetric matrices

We consider in this paper some applications of two problems to nonlinear control and linear algebra. Problem A concerns a skew symmetric matrix with elements belonging to a commutative algebra. It is desirable to minimize the matrix. Problem B concerns optimal decomposition for a skew symmetric matrix with complex elements and positive numbers. It is shown how one may obtain new spectral inequalities for matrices using an optimal control problem. The crucial point in this reduction is a time scalability property. We would like to point out here that as the development of linear control theory gave a push to the development of linear algebra, nonholonomic control theory will enrich polylinear algebra