Index Notation & Vectors | General Relativity

So far we have been dealing with things such as vectors, metrics & transformations in terms of matrices but it turns out that using matrices is not efficient for everything & for many objects you cannot even represent them with matrices. So why not develop a better way to write things down which is what I start with, discussing why matrices suck! Leading us to develop an index notation which I do with an example & mention some important properties of index notation, with all of this then we are ready to talk about space-time vectors. Now in this part our main goal will be to find the transformation law for vector components & basis vectors, I do that with an example.