This paper discusses a basic problem: Is the coordinate transformation coefficient the component of a tensor? The conventional viewpoint is that the coordinate transformation coefficient is not the component of a tensor. To reveal the essence of the coordinate transformation coefficient, the basic concept of the tensor is revisited. A new concept, i.e. the hybrid tensor, is defined. On the basis of the new concept, the conventional viewpoint is negated: the coordinate transformation coefficient is indeed the component of a tensor. That is to say, it is the hybrid component of a metric tensor. Thus, the concept of tensors is extented.
This paper reviews three excellent theoretical mechanics textbooks, published in the 1960's in China, with respect to the textbooks'general situation, the main contents, the characteristics, the scope of applications and the authors. They have been widely adopted by Chinese universities and colleges through several revisions. They are: theoretical mechanics I, II, by the Department of Theoretical Mechanics of Harbin University of Technology; theoretical mechanics, by Hao Tongsheng; theoretical mechanics, by the Department of Theoretical Mechanics of Zhejiang University.