Talk:Contravariant

Should this page be moved to contravariant tensor? Michael Hardy 22:19, 5 Apr 2005 (UTC)

There's actually already a plethora of articles discussing covariant and contravariant transforms, for instance, four-vector, Lorentz covariance, not to mention covariant transformation and contravariant transformation. I'm not sure which organization scheme I like, since four-vector makes the distinction between contravariant and covariant vectors, which are defined by how they transform, but as a physicist I'm still more likely to look up covariant or covariant vector before covariant transformation.--Laura Scudder | Talk 05:45, 2 May 2005 (UTC)

There's a really basic possible source of confusion here, to be noted. Towards the end it talks about pullback and covariance. Of course it is the 'components of' something covariant that pull back (act as something contravariant does); because 'components of' is coded language for dual space. It would be very good to get this properly phrased and highlighted on WP. Charles Matthews 09:39, 2 May 2005 (UTC)

Contravariant components are distantly related to covariant transformation so I think the article should not be merged. General covariance expresses the invariance of certain physical and mathematical quantities to coordinate system changes (including a change to a system in relative motion to the original), while covariant and contravariant components can be used in elasticity, optics and other places where covariance under transformations is of little interest. I added a bit to the page and apologize I could not find a help screen to bring in Greek so I spelled out "theta". Pdn 03:05, 12 May 2005 (UTC)