Strong ellipticity in elasticity ($c_{\alpha i\beta j}{m}_i{\nu }_{\alpha }{m}_j{\nu }_{\beta }>0$)

Strong ellipticity requires the displayed inequality for every nonzero displacement vector $m$ and material direction $\nu$. Equivalently, every acoustic tensor is positive-definite. It is weaker than positivity of the moduli on all matrices. A quadratic minor null Lagrangian vanishes on rank-one matrices, so adding such a term does not change the acoustic tensor or this condition.