Introduction to the properties of tensors

Abstract

This chapter introduces the notion of tensors in physics (field tensors and material property tensors), starting from the matrix of physical properties. The basic properties of vector spaces and the elementary mathematical properties of tensors are then recalled. The most important part of the chapter, Section 1.1.4, is devoted to the symmetry properties of tensors: Neumann's principle, Curie laws and the reduction of the components of polar and axial tensors of rank up to 4 for the 32 crystallographic groups. The relations between the thermodynamic functions and the physical property tensors are developed in Section 1.1.5.