- #1

Karl Karlsson

- 104

- 11

- Homework Statement:
- I am not completely sure what the formulas ##v_j = v^a\frac {\partial x^j} {\partial \chi^a}## and ##v^b = v^a\frac {\partial \chi^b} {\partial x^j}## mean. Is ##v_j## the j:th cartesian component of the vector ##\vec v## or could it hold for other bases as well? What does the second equation ##v^b = v^a\frac {\partial \chi^b} {\partial x^j}## mean? Is this just the relation between the b:th and j:th component of ##\vec v## being expressed as tangent vectors?

- Relevant Equations:
- ##v_j = v^a\frac {\partial x^j} {\partial \chi^a}## and ##v^b = v^a\frac {\partial \chi^b} {\partial x^j}##

I am not completely sure what the formulas ##v_j = v^a\frac {\partial x^j} {\partial \chi^a}## and ##v^b = v^a\frac {\partial \chi^b} {\partial x^j}## mean. Is ##v_j## the j:th cartesian component of the vector ##\vec v## or could it hold for other bases as well? What does the second equation ##v^b = v^a\frac {\partial \chi^b} {\partial x^j}## mean? Is this just the relation between the b:th and j:th component of ##\vec v## being expressed as tangent vectors?