- #1

- 1,068

- 0

I wasd beginning to feel at home with vectors and covectors but while trying to fully understand the concepts this query came up._________

Excuse the lack of rigorous definition but I think you will realize what I am aiming at.

Take a geometrical vector in a finite dimensional space and give it an oblique linear coordinate basis. Take this vector as not representing any physical quantity. Construct the dual basis. If we called the vector referred to the original basis a VECTOR, does it become a COVECTOR when referred to the dual basis.

If this is the case and as the first choice of basis was arbitrary, then the dual basis could have been chosen as the original basis ( ??? ) and the vector would be a VECTOR when referred to this basis and a COVECTOR when rerferred to the new dual basis.

I am not sure if my reasoning is correct. It seems too simple and I have a feeling that a metric will in some way be involved and invalidate this reasoning.

Matheinste