I'm having some trouble with 2 identitys from tensor calculus. I need to proof these two guys:
- in euclidean 3-dimensional space, an antisymmetric matrix with entries $M_{ij}$ is equivalent to a vector $v^k=\frac{1}{2}\epsilon^{kij}\,\,M_{ij}$
- the inverse formula is $M_{ij}=\frac{1}{2}\epsilon_{ijk}\,\,v^k$
I know that the levi civita symbol is totally antisymmetric, and so any other totally antisymmetric object Mij will be proportional to the levi-civita symbol, but I just cant see the two informations adding up.
I appreciate any hint!