I want to construct an additive compound matrix which has the following form as output :
ACM = {{a11 + a22, a23, -a13}, {a32, a33 + a11, a12}, {-a31, a32,
a33 + a22}}
Thanks.
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1$\begingroup$ What is the starting point? What are the rules that generate this matrix? $\endgroup$– MarcoBJan 13, 2022 at 17:38
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1 Answer
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Assuming you made a typo in ACM[[3,2]], and meant a21 instead of a32, your ACM is the generic form of the additive compound matrix of a $3\times 3 $ matrix (I took the definitions from this pdf):
CalcACM[matrix_, k_] := D[Minors[IdentityMatrix[Length@matrix] + t*matrix, k], t] /. t -> 0
mGeneric = {
{b11, b12, b13},
{b21, b22, b23},
{b31, b32, b33}
}
CalcACM[mGeneric,2]
(* {{b11 + b22, b23, -b13}, {b32, b11 + b33, b12}, {-b31, b21, b22 + b33}} *)
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$\begingroup$ Dear Hausdorff, thank you so much for your response and for sharing the reference of Muldowney as well. :) $\endgroup$ Jan 14, 2022 at 9:51