shankar@rnd.GBA.NYU.EDU (Shankar Bhattachary) (01/29/90)
In article <2011@onion.reading.ac.uk> ceb@onion.cs.reading.ac.uk (Colin Bridgewater) writes: >In article <62200002@hpl-opus.HP.COM> steinbac@hpl-opus.HP.COM (Gunter Steinbach) writes: >>The Kronecker delta is a discrete version of the Dirac delta function. :-) >> >>It is written as "delta sub ij", and its value is 1 for i=j and 0 for >>i!=j. >> >> Guenter Steinbach gunter_steinbach@hplabs.hp.com > > > >Hmmmmmm: sounds suspiciously like the identity matrix to me..... Any other >takers? It is just that. My exposure to the Kronecker delta has been in quantum mechanics, where it is used as a compact notation for the identity matrix in situations where the expressions are not sufficiently complex to rate matrix notation, and just get written out in full. In a domain where quantum and energy states are discrete, and so on, and one might be looking at just a few states, it is convenient to be able to write: x = y-sub-i + delta-sub-ij * z-sub-j to mean x = y-sub-i + z-sub-j for i = j and y-sub-i otherwise, rather than putting down a matrix representation. When you deal with more than one delta (as per the semantics of the indices), the notation is more intuitively obvious, at least to people who use it mostly in an intuitive way, with primary focus on the physical intuition. Not that anyone studying neural nets should care, but my 0.02 worth.... -------------------------------------------------------------------------- Shankar Bhattacharyya, Information Systems, New York University shankar@rnd.gba.nyu.edu --------------------------------------------------------------------------