Can the covariant components of a vector, v, be thought of as v multiplied by a matrix of linearly independent vectors that span the vector space, and the contravariant components of the same vector, v, the vector v multiplied by the *inverse* of that same matrix?(adsbygoogle = window.adsbygoogle || []).push({});

thinking about it like that makes it easy to see why the covariant and contravariant components are equal when the basis is the normalized mutually orthogonal one, for example, because then the matrix is just the identity one, which is its own inverse.

that's what the definitions i read seem to imply.

Thanks!

**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 question about interpretation of contravariant and covariant components

Loading...

Similar Threads - Quick question interpretation | Date |
---|---|

Quick Question about Smooth Maps | Oct 28, 2011 |

Quick question - Christoffel Symbol Transformation Law | Sep 11, 2011 |

(Hopefully)Very quick volume calculation question | Jun 9, 2011 |

Quick length of curve question | Feb 15, 2011 |

Quick question on formula | Jun 2, 2007 |

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