Therefore, the basie feature of Zhuangzhou s philosophy is the two-fold-in-one of the living outlook and ecological Outlook,such feature is mainly embodied in : expressing man s free nature by use of large ecological Outlook; the crux of such large ecological outlook is the protection and exploration of man s spirit ecology.

This paper considers the relationship between the twofold element for plane projective transformation and characteristic root of transformation matrix,and points out the existing conditions of the twofold point(the twofold line) and the twofold point range(the twofold line pencil).