Here I show same photos of my notes written on a witheboard or a sheet of paper that summarize some important considerations about:
- vector space,
- dual space (or one-form space)
- Tangent space on a point of a manifold
- Cotangent space.
- Euler Lagrange equations
A summary scheme followes about relationships between components of vectors, covectors and tensors, both in general case and tangent and cotangent spaces on a manifold: