Abstract: In this paper a matrix theorm is proved and two corollaries of it was given. On the above basis,a simpler proof of a equivalence theorm concerning dynamic equation equivalence and strict system equivalence is given. What is improtant is not the proof itself but a corollary obtained from the proof, for the corollary uncovers the real connection between the two sorts of equivalence, that is, the two seem not to be entirely equivalent. This allows the equivalence theorm to be stated in an exact form.

摘要： 本文首先建立了一个矩阵定理,给出了该定理的两个推论。以此为基础,对动态方程等价和系统严格等价的一个定理给出了简单的证明。但重要的不是这个证明本身,而是由此得出的一个推论。这个推论揭示了动态方程等价和严格系统等价之间的内在联系。结果表明,动态方程等价和严格系统等价的条件似乎并不完全等价。据此,文中给出了动态方程等价和严格系统等价定理的更准确的陈述。