# Einstein Notation

1. Jul 4, 2009

### Gear300

From what I'm reading, Xj = aijXi (X is a vector and the subscript for a is i)...though I'm not sure where the aijXi came from. Would this by any chance be a relation for the transformation equations from Xj to Xi?

Last edited: Jul 4, 2009
2. Jul 4, 2009

### HallsofIvy

Staff Emeritus
Yes, $x^j$ and $\underline{x}^i$ are vectors. $a_i^j$ is a mixed tensor of order 2. It's not clear to me what you mean by "given a vector summation" but on the right side of the equation there certainly is a summation: The "Einstein convention" is that when an index is repeated, once as a subscript and once as a superscript, you sum over all values of that index.

3. Jul 4, 2009

### Gear300

I see. Thanks for the assistance.