This note provides a short guide to dimensional analysis in Lorentzian and general relativity and in differential geometry. It tries to revive Dorgelo and Schouten’s notion of ‘intrinsic’ or ‘absolute’ dimension of a tensorial quantity. The intrinsic dimension is independent of the dimensions of the coordinates and expresses the physical and operational meaning of a tensor. The dimensional analysis of several important tensors and tensor operations is summarized. In particular it is shown that the components of a tensor need not have all the same dimension, and that the Riemann (once contravariant and thrice covariant) and Ricci (fully covariant) curvature tensors are dimensionless. The relation between dimension and operational meaning for the metric and stress–energy–momentum tensors is discussed; and the main conventions for the dimensions of these two tensors and of Einstein's constant are reviewed. A more thorough and updated analysis is available as a preprint.

本笔记提供了有关洛伦兹和广义相对论以及微分几何中的量纲分析的简短指南。它试图恢复 Dorgelo 和 Schouten 关于张量的“内在”或“绝对”维度的概念。内在维数与坐标维数无关，表示张量的物理和运算意义。总结了几个重要张量和张量运算的量纲分析。特别是它表明张量的分量不需要都具有相同的维度，并且黎曼（一次逆变和三次协变）和 Ricci（完全协变）曲率张量是无量纲的。讨论了度量和应力-能量-动量张量的维数和操作意义之间的关系；并回顾了这两个张量的维度和爱因斯坦常数的主要约定。更全面和更新的分析可作为预印本提供。