Alt Tensor: If Alt(\omega)=\omega, Is \omega Alternating?

[yifli]

If $\omega$ is an alternating tensor, then $Alt(\omega)=\omega$, where Alt is the mapping that maps any tensor to an alternating tensor.

I guess the converse is also true, i.e., if $Alt(\omega)=\omega$, then $\omega$ must be an alternating tensor. Am I right?

 

[Office_Shredder]

If you have w=Alt(w), and Alt(w) is an alternating tensor...