I have just starting learning relativity and I have still a problem with the definition and notation of tensors.(adsbygoogle = window.adsbygoogle || []).push({});

So a (r,s)-tensor takes r vectors, s one-forms and gives a scalar.

Then I understand that a (1,0)-tensor takes 1 vector (e.g. from V) and gives a scalar which is exactly the definition of a one-form (in V*), which corresponds to the mapping (V->R).

But I am still uncomfortable with the symmetrical situation, i.e. that a (0,1)-tensor is a vector. A (0,1)-tensor takes a one-form (e.g. u \in V*) and gives a scalar. But the one-form u given as argument is itself a mapping from V to R, so in a sense my (0,1)-tensor is a mapping ((V -> R) -> R) and instinctively I would "reduce" it to (V->R) or (V->RxR) but I cannot figure out how at the end it gives something which is again in V.

I am probably wrong in the vector spaces I consider, am I ?

Thanks a lot for your help.

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

Dismiss Notice

Join Physics Forums Today!

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

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

# Confusing (0,1)-tensor

Loading...

Similar Threads - Confusing tensor | Date |
---|---|

I Confusion about derivation for isotropic fluids | Sep 17, 2016 |

A Confused about stress-energy tensor | Jun 1, 2016 |

Little confused with tensor index manipulation | Feb 16, 2015 |

Weyl tensor in 2 dimensions- confused ! | Jul 5, 2013 |

Confused about the metric tensor | Jul 21, 2012 |

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