- #1
nigelscott
- 135
- 4
I am trying to figure how one arrives at the following:
dxμ∂ν = ∂xμ/∂xν = δμν
Where,
dxμ is the gradient of the coordinate functions = basis of cotangent space
∂ν = basis of tangent space
I know that dual vectors 'eat' vectors to produce scalars. Is this demonstrated by absorbing d into ∂ so that dxμ ≡ ∂νxμ or is such an operation illegal?
dxμ∂ν = ∂xμ/∂xν = δμν
Where,
dxμ is the gradient of the coordinate functions = basis of cotangent space
∂ν = basis of tangent space
I know that dual vectors 'eat' vectors to produce scalars. Is this demonstrated by absorbing d into ∂ so that dxμ ≡ ∂νxμ or is such an operation illegal?