How to Transform Dual Vector Fields: Understanding the Notation and Rules

[tourjete]

Homework Statement

Let va be a dual vector field. Show that the quantity ∂_[a v_b] transforms as a type (0, 2) tensor under coordinate transformations.

Homework Equations

w_u' = (dx^u / dx^u') w_u

The Attempt at a Solution

My main problem is that I don't know what the brackets mean.

I know if they weren't there it doesn't transform like a tensor because there's a second derivative when you do out the math and it's non-tensorial that way.

Does anyone know of a good online resource that describes how to transform vectors? My textbook doesn't give very concrete examples.

 

[HallsofIvy]

You seem to be saying that you are trying to do a problem involving "$\partial_{[a }v_{b]$" without knowing what it means. If so, then the first thing you should do it look it up! Where did you get this problem? If it is from a textbook, it will certainly be defined in the book. If you were give this problem by an instructor, ask the instructor. That is generally better than asking other people because they may have learned definitions that differ from the one you need to use.