Tensor is a geometric entity, or a generalized "quantity". Tensor concepts include scalar, vector and linear operators. Tensor can be expressed in coordinate system and recorded as scalar array, but it is defined as "independent of the choice of reference system"
Tensor concept is a generalization of vector concept and matrix concept. Scalars are zero-order tensors, vectors are first-order tensors, matrices (squares) are second-order tensors, while third-order tensors are like three-dimensional matrices, and higher-order tensors cannot be represented graphically.
The word "tensor" was first put forward by William Ron Hamilton in 1846, but he used this word to refer to an object called a module in modern times. The modern meaning of this word was started by Voldemar vogt in 1899. This concept was put forward by gregorio Ricci-Kubasto in 1890 with the title of Absolute Differential Geometry, and became known to many mathematicians with the publication of Levi-Civita's classic article Absolute Differential (in Italian, followed by other translations) in 1900. With the introduction of Einstein's general theory of relativity around 19 15, tensor calculus has been more widely recognized. General relativity is completely expressed in tensor language.
Tensor can be expressed as a series of values, which are represented by functions of vector range and scalar range. The vectors in these fields are vectors of natural numbers, and these numbers are called indicators.
A vector can be represented as a series of values, which are represented by the domain of scalar values and the function of the domain of scalar values. The number in the definition domain is a natural number, called an index, and the number of different indexes is sometimes called the dimension of a vector. A vector is a quantity defined in a linear space. When the basis of this linear space is transformed, the components of the vector are also transformed. Linear space is accompanied by dual space.