The components of the tensor $T^{i j}$ are: $T^{i j}=m\left(\omega^i \omega^j-\omega^2 \delta^{i j}\right)$ , where $\delta^{i j}$ is the Kronecker delta and $\omega^2=\omega^k \omega^k$.
The expression $T^{i j}=m\left(\omega^i \omega^j-\omega^2 \delta^{i j}\right)$ is the centrifugal force tensor in component form. It is derived by rearranging the equation for the centrifugal force, $F_c^i=m\left[\omega^i\left(\omega^j x^j\right)-\omega^2 x^i\right]$, into the linear tensor product form, $F_c^i=T^{i j} x^j$.
This tensor $T^{i j}$ mathematically encodes how the centrifugal force depends on the mass and rotation parameters, allowing the force $F_c^i$ to be calculated simply by multiplying $T^{i j}$ by the position vector $x^j$.