Sheppard W.F. From Determinant to Tensor

Oxford University Press, Oxford, 1923, 128 p.The tensor calculus used in the mathematical treatment of relativity, and concisely explained by Professor A. S. Eddington in his 'Report on the Relativity Theory of Gravitation', is, like the various kinds of vector calculus, a system of condensed notation which not only conduces to economy in the writing of symbols, but, what is more important, enables spatial and physical relationships to
be grasped as a whole without'having to be built up from a number of components which really represent views from different parts of space. Three-dimensional geometry or physics is troublesome enough: the addition of a fourth dimension made the need of a condensed notation imperative.Professor Eddington has recently pointed out that the tensor notation and methods can be applied, with happy results, to other and more elementary classes of problems than those for which they were originally devised; and this book is an attempt to put his somewhat compressed exposition into a form in which it may appeal to a larger circle of readers. The book, therefore, is not intended as an introduction to the mathematical theory of relativity — though I hope it may be of some use for that purpose — but rather as an exercise in the elementary application of
methods which, apart from any practical use, possess a special beauty of their own.