This isn’t a question that will be of interest to most science buffs here so I apologize if you wasted your time clicking on it. I’m hoping a mathematician or maybe Chronos will know the answer.
The above site says that given an Euclidean orthonormally represented vector
V = < 5 , 12 > you can define two new basis sets:
A[sub]1[/sub] = < .5 , 0 >
A[sub]2[/sub] = < .75 , .5 >
A[sup]1[/sup] = < .2 , -3 >
A[sup]2[/sup] = < .0 , 2 >
He then says that the first set is contravariant and the second set is covariant.
How can you have a covariant or contravariant basis set for fixed vector? And if you can, then what is that that makes them covariant and contravariant?