Dual - dual operator

allows one to calculate the dual operator on an expression (just rise and lower indexes in local coordinates)
  • expr - any tensor expression.
  • The operator has the following properties:
  • - The Dual operator is linear.
  • - For any vector field X in local coordinates we have: Dual(X)j=Xigij
  • - For any 1-form in local coordinates we have: Dual()i=jgji
  • - For any tensor fields and the following rule for dual operator takes place: Dual(T)=(Dual())(Dual(T))