ABSTRACT
A tensor of order one is a linear function that maps every vector into a scalar. A tensor of order two is a linear function that maps every vector into a vector. Tensors of higher order may be defined in a similar way. For instance, a tensor of order three is a linear function that maps every vector into a dyadic. The summation, multiplication by scalars, and dot product of tensors are governed by many of the same rules as in the arithmetic of real numbers. The definitions and properties to be stated are equivalent to well-known results of matrix theory. This chapter discusses some of the physical quantities characterized by tensors of order two and higher. Piezoelectricity or pressure electricity is a physical phenomenon that can be modeled with higher-order tensors.
