On the decomposition of complex vector spaces and the Jordan canonical form of complex linear transformations

New objects characterizing the structure of complex linear transformations were introduced. These new objects yield a new result for the decomposition of complex vector spaces relative to complex linear transformations and provide all Jordan bases by which the Jordan canonical form is constructed. Accordingly, they can result in the celebrated Jordan theorem and the third decomposition theorem of space directly and moreover, they can give a new deep insight into the exquisite and subtle structure of the Jordan form. The latter indicates that the Jordan canonical form of a complex linear transformation is an invariant structure associated with double arbitrary choices.EI011997-10032