- #1
binbagsss
- 1,254
- 11
I am just being introduced to the notion of covectors.
I see that the gradient of a scalar function is thought of as a covector.
Q1) On another source I have read to think of contravariant vector field as a differential operator: Va [itex]\partial _a[/itex] and to think of a covariant vector field as differential: wadxa.
From the fact that the gradient function is a covector, I thought this would be the other way around?
Q2) I'm trying to understand why df=[itex]\partial _a[/itex](f )dxa is a covector?
My thoughts:
[itex]\partial _a[/itex]f is a covector.
dxa is a vector.
So, isn't this just the definition of a contraction - multiplication of a covector and a vector to yield a scalar.
Thanks very much in advance.
I see that the gradient of a scalar function is thought of as a covector.
Q1) On another source I have read to think of contravariant vector field as a differential operator: Va [itex]\partial _a[/itex] and to think of a covariant vector field as differential: wadxa.
From the fact that the gradient function is a covector, I thought this would be the other way around?
Q2) I'm trying to understand why df=[itex]\partial _a[/itex](f )dxa is a covector?
My thoughts:
[itex]\partial _a[/itex]f is a covector.
dxa is a vector.
So, isn't this just the definition of a contraction - multiplication of a covector and a vector to yield a scalar.
Thanks very much in advance.