Theoretical physics is like a bouquet of roses (or particles you may say!). It has an enticing fragrance, which forces you to follow its fume, no matter how far you may have to go. And like a simpleton child you follow this fume with firm belief that you will, at the end, find a beautiful heaven-like garden of roses. But the fragrance is omnipresent, everywhere. There is not just one narrow path. The fragrance will some time take you to the notations of tensors, the principles of quantum world, the groups of Lie, the topology of rubber sheet, the geometry of Riemann, the relativity of Einstein, the standard model of Salam, the diagrams of Feynman, the symmetries of Noether, the diagrams of Dynkin.
Let is be a vector in 3-dimensional space. Is the set of all vectors with a vector space?
If two tensors have all their components equal in one coordinate system, then their components are equal in any of the coordinate systems.