坐标变换系数张量观与杂交张量概念分析<sup>1)</sup>

坐标变换系数张量观与杂交张量概念分析¹⁾

摘要: 本文致力于澄清一个十分基本的问题：坐标变换系数是否为张量?传统观念认为,坐标变换系数不是张量。为了揭示坐标变换系数的本质,本文采用“从一般到特殊”的研究策略,重塑了张量的内涵和外延,引入了杂交张量概念,进而颠覆了坐标变换系数不是张量的传统观念,确切地讲,它就是度量张量的杂交分量。这一结果扩张了张量概念的集合,提升了张量分析学内在的统一性、对称性和不变性,减少了连续介质力学的运算量。

Abstract: 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.