Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » Math Topics » alt.math.undergrad.independent

Topic: Index Notation Question - Help Needed
Replies: 0  

Advanced Search

Back to Topic List Back to Topic List  
David

Posts: 1
From: Redmond
Registered: 8/30/11
Index Notation Question - Help Needed
Posted: Aug 30, 2011 2:22 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

I am currently trying to learn Vector Notation.

I have recently been introduced to two rather abstract symbols. I consider them abstract because I have not seem them in my undergrad studies. These two symbols are the Kronicker Delta and the Levi-Civita Symbol.

I understand that these two symbols are essentially multipliers. I understand them best when they are used to calculate the dot product and the cross product of a vector. Thus far I have seen examples of these symboles notated as follows:

Delta Kronicker: dij, dji
Levi-Civita: Eijk, Ejki, Ekji, etc.
where d equals delta, and E equals epsilon.

My confusion begins with the following:

"The inverse of

di = (Eijk)Tjk

Where di is a "Dual Vector", and Tjk is a Tensor.

is found by multiplying both sides by Eilm, that is,

(Eilm)di = (Eilm)(Eijk)(Tjk)

I understand what Tjk is (T11, T12, T13, T21, T21, ... T33). However Eilm is new to me and I do not know what sets Eijk apart from Eilm. I am familiar with i, j, k because undergrad courses always used them as the x, y, and z axis. Is this why we start with Eijk? If so, what is Eilm? Eilm seems to be quoted in my text often, yet what is the lm in Eilm? for example:

(Eijk)(Eilm) = (djl)(dkm) - (djm)(dkl)

I can see further ahead in my text, Eipq, etc is used. Are these leters just arbitraty indices? If so, is Eilm just next in line?

Perhaps you can refer me to an online article or journal that may be able to explain these differences a bit better?

Thanks for the help.



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.