# Construction of an additive compound matrix

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.

• What is the starting point? What are the rules that generate this matrix? Jan 13 at 17:38

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}} *)

• Dear Hausdorff, thank you so much for your response and for sharing the reference of Muldowney as well. :) Jan 14 at 9:51