Greetings,(adsbygoogle = window.adsbygoogle || []).push({});

I have been going through Bernard Schutz’s “A First Course in General Relativity”, and I have a quick question on tensors. On page 73, the book defines an (M,N) tensor as “a linear function of M one-forms and N vectors into the real numbers”, which I’m fine with – I had no trouble with the problems at the end of the chapter. However, on page 57, it says “Notice that an ordinary function of position, f(t,x,y,z), is a real-valued function of no vectors at all. It is therefore classified as a (0,0) tensor”.

Why couldn’t (t,x,y,z) be thought of as a vector, since it is an ordered 4-tuple? This would make the position function f a one-form, so it would output a scalar after receiving the (t,x,y,z) vector as input - ie., would do exactly what the familiar f(t,x,y,z) does.

Basically, my question isn’t really about SR or GR at all, but more about the distinction between a vector and an ordered n-tuple in general – it previously seemed like just an arbitrary difference in ways of thinking about it to me, but now it seems like it and its relation to the difference between (0,0) tensors and (0,1) tensors, or (1,0) tensors for that matter, is important for distinguishing between these different types of tensors.

Thank you for any help you can give.

-HJ Farnsworth

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

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!

# Quick tensor question

Loading...

Similar Threads - Quick tensor question | Date |
---|---|

Quick Ricci tensor/scalar contraction manipulation question | Apr 17, 2015 |

Quick question tensor density transformation law | Apr 7, 2015 |

Quick one-line on lowering indices | Mar 1, 2015 |

Index notation tensors quick question | Jan 13, 2015 |

Quick question to clear up some confusion on Riemann tensor and contraction | May 2, 2011 |

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