O'Reilly logo

Vectors, Pure and Applied by T. W. Körner

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

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 imagesijk 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 ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required