Wednesday, June 21, 2017

vectors - Gradient is covariant or contravariant?



I read somewhere people write gradient in covariant form because of their proposes. I think gradient expanded in covariant basis $i$, $j$, $k$, so by invariance nature of vectors, component of gradient must be in contravariant form. However we know by transformation properties and chain rule we find it is a covariant vector. What is wrong with my reasoning?


My second question is: if gradient has been written in covariant form, what is the contravariant form of gradient?




No comments:

Post a Comment

classical mechanics - Moment of a force about a given axis (Torque) - Scalar or vectorial?

I am studying Statics and saw that: The moment of a force about a given axis (or Torque) is defined by the equation: $M_X = (\vec r \times \...