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For we have for each component
of the grad operator,
This follows from row 1 of the matrix
Summation over is implied.
For it is unambiguous to write all components
together as a vector relation thus,
This follows from the singular solution
for the first unit vector .
It is interesting that the equal wavenumber case involves one order
of derivative less than the unequal case.
In the Dirichlet BC case, (H.21) vanishes.