Explanation of this matrix differential equation In one book I have found the equation: $$ \bigtriangledown\cdot (De^{-irk(t)})=-k(t)^{T}Dk(t), $$ where k is a 3d vector, r=[x,y,z] and D is a 3x3 matrix. I don't understand at all how to get the RHS from the LHS of the equation but it is crucial to understand some problem. Could you please explain me this? I would appreciate details. It is eq. [6A.10] from "Diffusion MRI Theory, Methods, and Applications" by Derek K. Jones (2011), page 88. Available here:

Here: $$ \
abla \cdot (D\
abla\psi)= (-{\rm i})\
abla \cdot (D\psi \vec{k})=(-{\rm i})\sum_i \frac{\partial}{\partial x_i}(D\psi \vec{k})_i=(-{\rm i})\sum_{i,j} \frac{\partial}{\partial x_i}D_{ij}\psi k_j$$

$$=-\sum_{i,j} D_{ij}\psi k_ik_j=-(k^TDk)\psi$$