# Outer product of two one forms.

1. Nov 13, 2004

### ronblack2003

Given two one forms f = (1,1,0,0,) and g=(-1,0,1,0): what are the components of f(x)g ... would appreciate any help.

2. Nov 13, 2004

### ronblack2003

Outer Product of two One Forms

Given two one forms f = (1,1,0,0) and g = (-1,0,1,0):
What would be the Components of f(outer product)g be?
would appreciate any help.

3. Nov 14, 2004

### pervect

Staff Emeritus
I'm not quite sure if the "outer product" is the wedge product or the tensor product. Wikipedia seems to think it's the former. See

The wedge product of u ^ v is

u (tensor) v - v (tensor) u

The intent here is to anti-symmetrize the tensor product, The formula above works as written only for rank 1 tensors (but that's what you have).

The tensor product p = u (tensor) v in component notation for rank 1 tensors is:

pij = uivj

Thus (1,2,3) (tensor) (4,5,6) is the second rank tensor (you can think of it as an array)

1*4 ,1*5, 1*6
2*4, 2*5, 2*6
3*4, 3*5, 3*6

Hope this helps

4. Nov 16, 2004