- #1
davidge
- 554
- 21
So, most Relativity textbooks (although some famous, like Weinberg's don't) show us that a vector ##V## is properly written as $$V^\mu(x) \frac{\partial}{\partial x^\mu}$$ where ##V^\mu(x)## are its components at the point ##x## and the "base" in which the vector is written in is the operator ##\frac{\partial}{\partial x^\mu}##.
But... is it useful to write the basis vectors as in above? Why are vectors written in that way in Special and General Relativity and not in other fields of physics and mathematics? e.g. in elementary vector calculus, vector analysis and linear algebra courses we usually don't write the basis vectors as partial derivative operators. Actually, I have to say the only place I have seen basis vectors represented in that way is in Special Relativity and in General Relativity.
But... is it useful to write the basis vectors as in above? Why are vectors written in that way in Special and General Relativity and not in other fields of physics and mathematics? e.g. in elementary vector calculus, vector analysis and linear algebra courses we usually don't write the basis vectors as partial derivative operators. Actually, I have to say the only place I have seen basis vectors represented in that way is in Special Relativity and in General Relativity.