对偶基矢量组在张量分析中的作用与意义

On the function and significance of dual bases in tensor analysis

在数学上将客观定律用量的分量形式表达为对坐标系具有不变性的方程，是张量分析所要解决的核心问题．为此，需从单一的基矢量组发展为对偶的两个基矢量组．文中给出了对偶基几何意义解释的新证明，进一步阐明了“同变”与“逆变”的含义，说明“同变”较之现在广泛使用的“协变”，是更为恰当的译名．

It is emphasized that the key problem in tensor analysis is to establish the mathematical equations of physical laws which are invariable when the coordinate system is changed. For this reason, two bases (natural basis and dual basis) should be introduced. The geometric meaning of dual basis,namely,e i=x i,is shown by a new demonstration. The meanings of 'covariant” and “contravariant” in tensor analysis are dicussed in detail.