Origin Of The Concept Of Tensor And Establishment Of Tensor Analysis

Tensor analysis plays an important role in math and physics. People have regarded tensor analysis gradually, because of the success of general relativity theory. Moreover, tensor analysis has been applied in more fields due to the foundation of gage theory and subtense theory. But the theory had hardly been researched yet. However, this paper offers many new discoveries on the basis of digging, collection, arrangement and analysis tensor math original documents, and hackling, researching and discussion tensor math phylogeny by means of conception analysis methods.First, original documents of vector's algebra definition has been found, Which is a clue for researching tensor math phylogeny. This expanding tensor cannot exceed three-dimensional condition without algebra definition of vector. Tensor is a higher dimensional math quantity, so algebra definition of vector is an important role for the foundation of tensor concept. But this content has been ignored in tensor math history.Secondly, analyse electromagnetics origin of tensor concept. Expatiates the history process of tensor concept from electromagnetics origin. But in the past, the traditional ideas of tensor concept origin are from mechanics. In fact, applied mechanics does not have important relations with tensor concept origin. The most important discovery of the paper confirms the first scholar who uses "tensor" in modern sense. Paper expatiates the foundation process of tensor analysis from non-Euclidean space ideas, Gauss' intrinsic ideas, n-dimensions manifold of Riemann, higher dimensional space idea of Grassmann, n-dimensions vector space idea of Cayley. As a kind of math methods to solve the problem of differential coefficient operation of curvilinear coordinates series, tensor analysis was origin from Gauss' intrinsic ideas. But Riemann is actually the first person advance this problem. His ideas of n-dimensions manifold advance quadratic differential form change problem of curved space in detail. This is the source toward tensor analysis. Subsequently, this method has been founded by the development of Beltrami, Christoffel, Ricci and so on.By way of complementarities, the application history of tensor analysis is explained briefly, which include Einstein and Hilbert gravitational field equation, and Weyl Levi-Civita Riemannian geometry. The new discovery here is textual researches the earliest appearance of Riemannian geometry.The creation of relies on algebra and geometry liberation in 19^th century. Tensor analysis creates on the basis of non-Euclidean geometry and abstract algebra appearance. Moreover, tensor analysis and Riemannian geometry developed deeply which promotes modern math development further. This research makes a profound sense on tensor math history.