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. . .
In that university textbook the V=B*Q matrix is introduced in
the context of the principle of superposition. Then the authors
say: "SOLVING THESE EQUATIONS WITH RESPECT TO
CHARGES, one can see that, inversely, charges are linear
functions of potentials." . . .
It would be interesting to trace the origin of the misconception . . .
. . . It is true
that linear relations exist between charges and potentials in both
ways (when Q are independent variables, and when V are
independent variables). What is not true is that Cij can be
calculated from Bij, or vice versa, by the matrix inversion
method. . . .