Can the Relationship Between Levi-Civita Tensor and Kronecker Symbol Be Proven?

[raopeng]

In many physics literature I have encountered, one of the properties of Levi-Civita tensor is that ε_{ijk}ε_{lmn}is equivalent to a determinant of Kronecker symbols. However this is only taken as a given theorem and is never proved. Is there any source which has proven this property?

 

[dextercioby]

Well, the tensor product is a six index object which is always expressible as a sum of a tensor product of 3 2-index objects which must necessarily be the delta Kroneckers. The nice arrangement of this sum in a determinant cannot be proven per se, just taken for granted.

 

[raopeng]

I can get that intuitively the Levi-Civita tensor is deeply connected to the Kronecker symbol. But if the arrangement cannot be proved per se, how does this theorem hold true...