On arbitrary sequences of isomorphisms in $R^{m}\rightarrow R^{m}$

Abstract:

In this paper a new, clean proof of an algebraic theorem needed in ordinary differential equations is presented. The theorem involves the existence and uniqueness of a “complete splitting” for some subsequence of an arbitrary sequence of isomorphisms of Euclidean m-space. In the positive-definite case, a complete splitting is a limit condition on eigenspaces and eigenvalues.