- #1
AxiomOfChoice
- 533
- 1
I've already posted a couple of index notation questions on here and I've gotten very helpful responses. So I thought I'd try my lucky again, though I'm a little more stumped on this question than I was on the others...
Let [itex]\vec{x}[/itex] be the position vector and [itex]\vec{r}[/itex] the radial unit vector. In index notation, I find myself confronted with simplifying
[tex]
x_k \partial_i r_k.
[/tex]
I desperately want this to be zero, but I can't figure out why it should be. (I can't really figure out what this represents at all, as a matter of fact.) Isn't [itex]\partial_i r_k[/itex] a 2 by 2 matrix? And if so, how would multiplying with [itex]x_k[/itex] make everything go away? Again, maybe it doesn't.
Can anyone help?
Let [itex]\vec{x}[/itex] be the position vector and [itex]\vec{r}[/itex] the radial unit vector. In index notation, I find myself confronted with simplifying
[tex]
x_k \partial_i r_k.
[/tex]
I desperately want this to be zero, but I can't figure out why it should be. (I can't really figure out what this represents at all, as a matter of fact.) Isn't [itex]\partial_i r_k[/itex] a 2 by 2 matrix? And if so, how would multiplying with [itex]x_k[/itex] make everything go away? Again, maybe it doesn't.
Can anyone help?