The component form of the centrifugal force, derived from the vector triple product expansion, is expressed as $F_c^i=m\left[\omega^i\left(\omega^j x^j\right)-\omega^2 x^i\right]$. This structure allows the force to be rewritten in the linear tensor product form $F_c^i=T^{i j} x^j$, where the $x$-independent term defines the centrifugal force tensor as $T^{i j}=m\left(\omega^i \omega^j-\omega^2 \delta^{i j}\right).$ This tensor T elegantly encodes the dependence of the centrifugal force on the mass ( $m$ ) and angular velocity ( $\omega$ ), using the Kronecker delta $\left(\delta^{i j}\right)$, and importantly, this resulting tensor $T^{i j}$ is symmetric because both $\omega^i \omega^j$ and $\delta^{i j}$ are symmetric with respect to the indices $i$ and $j$.
<aside> ❓