Hello. Apologies if this is in the wrong forum. This seemed the most relevent. I'm learning math a little late in life and am just now at one-forms. This is just a general question relating to that subject. I was hoping that somebody could explain the process of calculating a one-form relative to an arbitrary basis. For example, a basis:

e1 = 0, 1, 0 (relative to x1, x2, x3)

e2 = -1,-1, 0

e3 = 0,0,1

If w=dx1, than what is w relative to the above? What would dw be? Any help or an example would be appreciated.

Also, what if w is more complicated? w=x2*dx1 (or any function really).