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Suppose I have a matrix M=$\begin{pmatrix} A(p) & B(p) \\ C(p) & D(p)\end{pmatrix}$.

I want to apply some operatorial matrix E such that

EM=$\begin{pmatrix} 0 & \partial_p & \\ \partial_p & 0\end{pmatrix}\begin{pmatrix} A(p) & B(p) \\ C(p) & D(p)\end{pmatrix}$.

How can I create such an operatorial matrix ? I cannot do this explicitly because M is a product of complicated matrices, and I have to apply E several times.

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    – bbgodfrey
    Commented Jun 8, 2015 at 13:36
  • $\begingroup$ Perhaps you could carry out the product normally like a matrix product then replace the Times's at the right levelspec with the action of the operator or with an Apply. I'm not qualified to give an answer on pattern matching though... $\endgroup$
    – Histograms
    Commented Jun 8, 2015 at 13:46
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    $\begingroup$ Inner[Operate, {{(0 &) &, Derivative[1]}, {Derivative[1], (0 &) &}}, M, Plus]. Use Nest[] as needed. $\endgroup$
    – J. M.'s missing motivation ♦
    Commented Jun 8, 2015 at 14:01

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