Derivations and presentations of results in this book will appear in the tensor components, or in the related matrix notation. In the tensor component or subscript notation, vectors or first-order tensors are denoted by lower case italics with a single letter subscript, such as \( {n_i} \) or \( {\nu_j} \), while second, third and fourth-order tensors are written as \( {\varepsilon_{\textit{ij}}},\,\,{ \in_{\textit{ijk}}},\,\,{L_{\textit{ijkl}}} \), with the number of subscripts indicating the order or rank R of the tensor. The subscripts have a certain assigned range of values, which is i, j,… = 1, 2, 3, or \( \rho = 3 \) for tensorial quantities in the Cartesian coordinates \( {x_i} \). The number of tensor components is \( N = {R^{\rho }} \). It is then convenient to write the components of a first, second or fourth order tensors as \( {(3} \times {1),}\,\,{(3} \times {3)}\,\,{\text{\; or (9}} \times {9)} \) arrays, which need not conform to the rules of matrix algebra. The third order tensor can be displayed in three \( {(3} \times {3)} \) arrays.