Can anyone explaine Einstein Summation Notations?

Answer 1

Sure, why do you ask?

Answer 2

peri-renna did a fairly good job of explaining it. There are a couple of other rules that are typically seen:

1) Indices to be summed over usually have one upper and one lower index. So the example given should be
u_i v^i =u_1 v^1 +u_2 v^2 +u_3 v^3.
This rule is often violated in lower level courses, but is rigidly observed when doing general relativity.

2) If the space you are working in is not three dimensional, the summation goes from 1 to the dimension n.

Answer 3

Yes but....

without a text editor to do sums and superscripts and subscripts it is really hard.

Basically it is just shorthand for summation and is call the summation convention. It says that when an index appears twice in an expression it is ASSUMED that the expression represents a summation over that index.

Answer 4

The present Wikipedia article does a fair job - in general, there are two rules to remember:

* If, in a term in an equation, an index appears twice, then it is a dummy index. The term containing the dummy index represents a sum of terms with the dummy index replaced with each of the possible values (e.g. 1, 2, 3.)

Example: u_i * v_i = u_1 * v_1 + u_2 * v_2 + u_3 * v_3 (in 3-space).

* If, in _all_ terms in an equation, the same index appears exactly once, then that index is a free index. The _equation_ with a free index represents three equations - one for each value of the index.

Example: u_i = v_i implies u_1 = v_1, u_2 = v_2, and u_3 = v_3 (in 3-space).

If an equation doesn't fit those rules - for example, u_i = v_i*w_i, which has one i in the first term and two in the second - it's probably badly formed. (In my example, i is both a dummy and a free index, which is impossible.)

Good luck!

Answer 5

If you can't understand his notations you won't understand my explanation.