Is an Antisymmetric 4-Tensor Zero if Any Off-Diagonal Component is Zero?

[jeckster]

Homework Statement

prove the zero component lemma for any anti-symmetric 4-tensor: If anyone of its 0ff-diagonal component is zero in all inertial coordinate system, then the entire tensor is zero.

Homework Equations

The Attempt at a Solution

in case of 4-vector, if a particular component is zero in all inertial frame then by Lorentz Transformation in different direction, it can be proved that the 4-vector is zero in all inertial frame.
Here, i m confusing in how to prove it in case of anti-symmetric 4-tensor

Any help would be highly appreciated. thank

 

[crimsonidol]

I have the same problem. No answers yet.
off diagonal components of the antisymmetric 4 tensors in special relativity involves 3 vectors and we can form 4 vectors from them. If any component of that 3 vector is zero under LT the 4-vector is zero then all the off-diagonal terms are zero. This is what I thought but how can I express this in Mathematical Language?
If I'm wrong can you give me a clue about it?