three symbols i can't understand in relativity textbooks.?

Question

There are three symbols in relativity textbooks that I've never encoutered before and need lots of help with.

1.Einstein summation convetion : Though not really a symbol i still don't quite understand what is meant by it.

2. Upper case lambda with super scripts and subscripts: It seems to be some sort of linear transformation, but I still don't quite understand it.

3. The great demon, the kronecker delta: I really cannot understand what is meant by this.

The reason I have such a hard time with this notation is because I have very little formal education.

However after the symbols are understood, it becomes very lucid.

Can someone please give me a CLEAR and informal description of what this means with examples relating to relativity and tensor analysis?

PS. I don't want some freaking link to wikipedia! Those have no useful information and seem to me like an attempt at increasing the number of questions you answer.

Answer 1

I confess all (or most) of what I know about this, I learned from Wikipedia. Here's my attempt (and ^ means superscript, and not necessarily exponentiation):

1. The number i here is not defined as anything, so it is a counter, where f(x^i) = Sum(x_i) where i starts at 1 (or 0 in some texts, where a start of 1 is used for Greek letters), and goes to n, or whatever the predefined upper limit.[1]

Now, to represent vectors, the same idea is used, except this time, we are demonstrating what the index of the vector is, rather than adding them up. Thus, u^i = (u_1, u_2, ..., u_n) = [u_1 u_2 ... u_n]^T (a column vector). And v_j = [v_1 v_2 ... v_n] (a row vector).[2]

You get the idea. Basically it means repeat for each applicable i, and (in your case) add the results.

2. I was unable to find anything on Λ, except for something on astronomy, which I doubt would be what you were looking for. Perhaps you want Einstein notation for using the Von Mangoldt function?

3. You might think of delta_ij as being the value of the jth entry in the ith row of any sufficiently large identity matrix, since it has 1s down the diagonal, and 0s elsewhere.

A formal definition is delta_ij = 1 (if i = j) or 0 (if i != j), or using the Iverson bracket, delta_ij = [i = j].[3]

Thus, delta_46 = 0, but delta_77 = 1.

~~~
Sorry about #2. I guess 2/3 isn't bad!

Answer 2

I nonetheless do no longer think of we are able to comprehend the Holy Trinity. that doesn't advise we could continually provide up. It in easy terms potential that the Trinity is an inexhaustable secret to be pondered upon. I hate to be a stickler, yet i do no longer think of you have gotten it particularly suitable. you assert ''one nature.'' One nature could be one will. that is to disclaim that Christ has the two a human and divine nature, which could be an historical heresy called Monothelitism. are not getting me incorrect nonetheless... i do no longer advise it in a condemning style of way. I in basic terms think of that according to threat you're able to come across a distinctive term different than ''nature.'' it is incredibly basic to slip into heresy whilst describing the Holy Trinity, which it incredibly is suited to no longer clarify those issues in our very own words. i might inspire you to proceed pondering this, yet attempt to no longer be too hasty on your motives, and according to threat seem over the Athanasian Creed some extra cases. nonetheless, i'm going to provide you a famous person and a pat on the decrease back on your efforts. you have accomplished a miles extra advantageous activity with your clarification than i'm going to have. Peace, Drew playstation : to those that say the be conscious ''Trinity'' is not any found in the Bible (and there will be some), it is not proper whether it incredibly is or no longer. The Bible become canonized around Trinitarian doctrine, that's why the theory is there, whether we don't care to renowned it. St. Athanasius and St. Nicolas (specific, Santa Claus) defined the Trinity extra needless to say based on Bishop Arius, who taught that Jesus become in basic terms ''a robust guy.''

Answer 3

http://www.amazon.com/gp/reader/0070334846/ref=sib_dp_pt/104-2479740-8363901#reader-link
You can see the first chapter of this book on line. It will answer many of your questions. You need to get a book on tensors and learn a little math to understand relativity.