Abstract: A condition of transforming general linear dynamical systems into linear Birkhoffian dynamical systems is studied. The condition and the procedure of transformation is given and proved. A theorem of the equivalence between linear Birkhoffian systems and linear Hamiltonian systems is given. According to the condition given by using the Jordan form, the non-degenerate condition of the Birkhoff tensor is analyzed from several aspects.

Key words: linear dynamical systems, Birkhoffian equations, Hamiltonian equations, Jordan form

摘要： 研究一般线性动力系统何时转化为线性自治Birkhoff动力系统的问题，给出线性自治Birkhoff动力系统与线性自治Hamilton动力系统等价性的定理，并推导出2n维线性动力系统转化为线性自治Birkhoff动力系统条件，通过运用若当形对转化条件进行分析，分情况给出Bikhoff张量非退化的条件。

关键词: 线性动力系统, Birkhoff方程, Hamilton方程, 若当形