"The(adsbygoogle = window.adsbygoogle || []).push({}); componentsof a vector change under a coordinate transformation, but thevectoritself does not."

ie:

V = a*x + b*y = c*x' + d*y'

Though the components (and the basis) have changed, V is still = V.

Question 1:

Is that right?(I'm assuming so, the main Q is below)

Tensor rank (according to wolfram)

"The total number of contravariant and covariant indices of a tensor."

It is commonly said

"A vector is a tensor of rank 1"

Does this mean (A):

T^a, and R_a

are tensors of rank one

or does it mean (B):

V = (T^a)(R_a) is a tensor of rank one?

If it is (A), then how can a vector be regarded as a tensor of rank 1, when it is

(contravariant components)*(covariant basis)

I'm able to do the maths, but the terminology of 'rank' has been bugging me!

**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!

# Simple question on invariants and tensor rank

Loading...

Similar Threads - Simple question invariants | Date |
---|---|

A Simple metric tensor question | Aug 14, 2017 |

Symmetry of connection coefficients? (simple question) | May 22, 2013 |

Simple Geometry Question about a Complex Situation -Spherical/3D cartesian | Jan 25, 2012 |

Very simple question about homology | Apr 6, 2011 |

Simple Question on Homotopy Equiv. and Contractible Subspaces | Jan 18, 2011 |

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