- #1
TupoyVolk
- 19
- 0
"The components of a vector change under a coordinate transformation, but the vector itself does not."
ie:
V = a*x + b*y = c*x' + d*y'
Though the components (and the basis) have changed, V is still = V.
Question 1:
Is that right? (I'm assuming so, the main Q is below)
Tensor rank (according to wolfram)
"The total number of contravariant and covariant indices of a tensor."
It is commonly said
"A vector is a tensor of rank 1"
Does this mean (A):
T^a, and R_a
are tensors of rank one
or does it mean (B):
V = (T^a)(R_a) is a tensor of rank one?
If it is (A), then how can a vector be regarded as a tensor of rank 1, when it is
(contravariant components)*(covariant basis)
I'm able to do the maths, but the terminology of 'rank' has been bugging me!
ie:
V = a*x + b*y = c*x' + d*y'
Though the components (and the basis) have changed, V is still = V.
Question 1:
Is that right? (I'm assuming so, the main Q is below)
Tensor rank (according to wolfram)
"The total number of contravariant and covariant indices of a tensor."
It is commonly said
"A vector is a tensor of rank 1"
Does this mean (A):
T^a, and R_a
are tensors of rank one
or does it mean (B):
V = (T^a)(R_a) is a tensor of rank one?
If it is (A), then how can a vector be regarded as a tensor of rank 1, when it is
(contravariant components)*(covariant basis)
I'm able to do the maths, but the terminology of 'rank' has been bugging me!