the Kronecker delta

by newton1
Tags: delta, kronecker
newton1 is offline
Sep17-03, 11:00 AM
P: 152
i need help....[:(]
prove SUM(k) [E(ijk)E(lmk)]= d(il)d(jm) - d(im)d(jl)
where "d" is Kronecker delta symbol and "E" is permutation symbol or
Levi-Civita density
Phys.Org News Partner Science news on
Internet co-creator Cerf debunks 'myth' that US runs it
Astronomical forensics uncover planetary disks in Hubble archive
Solar-powered two-seat Sunseeker airplane has progress report
HallsofIvy is offline
Sep18-03, 05:28 AM
Sci Advisor
PF Gold
P: 38,904
A clarification: the Kronecker delta, d(ij), is 1 if i= j, 0 otherwise.

The Levi-Civita permutation symbol, E(ijk) {real notation is "epsilon"), is 1 if ijk is an even permutation of 123, -1 if ijk is an odd permutation of 123, and 0 otherwise. While d(ij) is defined for all dimensions, E(ijk) implies that i, j, and k can only be 1, 2 ,3. For higher "dimensions" we would need more indices.

SUM(k) [E(ijk)E(lmk)]= E(ij1)E(lm1)+ E(ij2)E(lm2)+E(ij3)E(lm3)

Register to reply

Related Discussions
HARD problem on mathematical problem and fourier series Math & Science Software 0
[SOLVED] Thermal Stress Problem + Tensions Problem Engineering, Comp Sci, & Technology Homework 4
Problem with find angle btw vectors (magnetism problem) Introductory Physics Homework 2
Is Mexico's racism problem driving the U.S. immigration problem? Current Events 8
Having a problem with a fairly early Physics with Calculus 1 problem Introductory Physics Homework 4