Transverse-traceless tensor
= Transverse-traceless tensor
{title2=$k_ih_{ij}=0,\quad h_{ii}=0$}
A transverse-traceless spatial tensor is orthogonal to its <Fourier mode> wavevector in each index and has zero trace. The <transverse-traceless projector> extracts this part. Trace terms and symmetrized coordinate-displacement gradients have no such part, explaining the linear gauge invariance of <tensor cosmological perturbations>.