Characterization of the class of canonical forms for systems of linear equations

Abstract: The equivalence group is determined for systems of linear ordinary differential equations in both the standard form and the normal form. It is then shown that the normal form of linear systems reducible by an invertible point transformation to the canonical equation $\by^{(n)}=0$ consists of copies of the same iterative equation. Other properties of iterative linear systems are also derived, as well as the superposition formula for their general solution.