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lang-mma
fandgare some functions onxor not? What are they? $\endgroup$df = (D[#, {x, 1}] + (-D[#, {x, 2}]) &);,dg = (D[#, {x, 1}] + (-D[#, {x, 2}]) &);,mat = {{df, dg}, {dg, df}},vec = {u[x], v[x]}, thenCenterDot[mat, vec]works, withCenterDotgiven in the former of the linked questions. This is withoutfandgbut adding them should be very straightforward. $\endgroup$Constructcan be used, e.g.,Inner[Construct, {{a # &, \!\( \*SubscriptBox[\(\[PartialD]\), \(x\)]#\) &}, {\!\( \*SubscriptBox[\(\[PartialD]\), \(y\)]#\) &, d # &}}, {u[x, y], v[x, y]}]. $\endgroup$