NOTE 1 For a given orthonormal base, a tensor $T$ of the second order can be represented by $n^2$ components $T_{ij}$, generally presented in the form of a square matrix, such that $T$ attributes to the pair of vectors U and V the scalar ${\displaystyle \sum _{i,j=1}^n{T}_{ij}}{U}_i{V}_j$, where $U_i$ and $V_j$ are the coordinates of vectors U and V.

NOTE 2 A tensor of the second order can be defined by a bilinear form applied to two vectors (covariant tensor), to two linear forms (contravariant tensor), or to a vector and a linear form (mixed tensor). This distinction is not necessary for a Euclidean space. It is also possible to generalize to tensors of order n defined by n-linear forms and for which the components have n indices. Tensors of order 1 are considered as vectors and tensors of order 0 are considered as scalars.

NOTE 3 A tensor is indicated by a letter symbol in bold-face sans-serif type or by two arrows above a letter symbol: T or $T$ ou $\overrightarrow{\overrightarrow{T}}$. The tensor $T$ with components $T_{ij}$ can be denoted $(T_{ij})$.

NOTE 4 A complex tensor $T$ is defined by a real part and an imaginary part: $T=A+jB$ where $A$ and $B$ are real tensors.