= Solution
{c}
For a nondegenerate band $E(\mathbf k)$, define the <reciprocal effective mass tensor> by
$$
\boxed{(M^{-1})_{ij}=\frac1{\hbar^2}\frac{\partial^2E}{\partial k_i\partial k_j}.}
$$
It is the curvature tensor of the <energy band>. Near an extremum, $E\simeq E_0+\hbar^2\delta\mathbf k^TM^{-1}\delta\mathbf k/2$, so positive principal curvatures give positive electron <effective masses>. Together with the <group velocity> $\mathbf v=\hbar^{-1}\nabla_{\mathbf k}E$ and $\hbar\dot{\mathbf k}=\mathbf F$, it yields $\dot v_i=(M^{-1})_{ij}F_j$. Negative electron curvature at a <valence band> maximum is conventionally recast as a positive <band effective mass> for missing electrons.
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