Hi all! I've got a short question concerning a minor notational issue about tensor contraction I've run across recently.(adsbygoogle = window.adsbygoogle || []).push({});

Let A be an antisymmetric (0,2)-tensor and S a symmetric (2,0)-tensor.

Then their total contraction is zero: [itex]C_1^1C_2^2\,A \otimes S=0[/itex].

As a proof one simply computes: [itex]A_{ij}S^{ij}=-A_{ji}S^{ji}=-A_{ij}S^{ij}[/itex]

When I first saw this, I was a bit confused about the second equality. Of course, a scalar is a symmetric tensor…but is it not an abuse of notation? I mean this seems to run into conflict with the way one handles components of antisymmetric tensors…as for me, for someone who's just got accustomed to the components manipulation machinery, I was disturbed when I saw this. Am I alone?

This is not a big deal…but are there alternatives to expressing stuff like that? Any comments?

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Contraction of Tensors

Loading...

Similar Threads - Contraction Tensors | Date |
---|---|

Is This Contraction of a Tensor Allowed? | Jul 17, 2015 |

Can contraction of a tensor be defined without using coordinates? | Aug 31, 2013 |

Contracting tensors | Mar 19, 2013 |

Contraction of a tensor | Oct 7, 2007 |

Understanding tensor contraction | Jul 15, 2007 |

**Physics Forums - The Fusion of Science and Community**