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10

More on tensors

10.1 Some tensorial theorems

This section deals mainly with tensors having special properties. We first look at isotropic tensors. These are tensors like δij and ijk which remain unchanged under rotation of our coordinate system. They are important because many physical systems (for example, empty space) look the same when we rotate them. We would expect such systems to be described by isotropic tensors.

Theorem 10.1.1 (i) Every Cartesian tensor of order 0 is isotropic.

(ii) The zero tensor is the only Cartesian tensor of order 1 which is isotropic.

(iii) The isotropic Cartesian tensors of order 2 have the form λδij with λ ...

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