On the minimal polynomial base for null spaces of a transfer function matrix and its defect

In this paper, through two examples, a method for solving the minimal polynomial base of (left/right) null spaces of a transfer function matrix (in brief, TFM), is introduced. Via this method, we can easily find the left/right minimal Kronenker indices. Therefore, the defect of a TFM could be rapidly computed. We also give a necessary and sufficient condition for the defect of a TFM to be zero. Errors in the related literatures are reviewed and revised.