Proof That Any Skew Symmetric Thrid Order System Has at Most One Non Zero Distinct Component
Letbe a completely skew symmetric third order systemwithcomponents.
Consider any component with at least two identical indices egInterchanging any two components changes the sign so that
The only possible non zero components are those with no indices being equal
The only possible components are a)123 , a)132, a_213, a_231, a_312 , a_321 .
But sinceis skew symmetricand there is at most one non zero component.