Abstract
In this chapter, we will consider methods for estimating the norm of a matrix and matrix exponents. The conditions for the existence and uniqueness of solutions are considered for ordinary differential equations using the Lipchitz conditions. Adjoint systems are revisited together with the application of the Carathedory theorem to some selected problems.
Keywords:
Adjoint systems, Carathedory theorem, Lipchitz conditions, Matrix exponents, Ordinary differential equations, Uniqueness.