Compound matrix

Compound Matrix

The kth compound matrix of A[m#n] is the m!(k!(m-k)!)-1#n!(k!(n-k)!)-1 matrix formed from the determinants of all k#k submatrices of A arranged with the submatrix index sets in lexicographic order. Within this section, we denote this matrix by Ck(A).

C1(A) = A Cn(A[n#n]) = det(A) Ck(AB) = Ck(A)Ck(B) Ck(aX) = akCk(X) Ck(I) = I Ck(AH) = Ck(A)H Ck(AT) = Ck(A)T Ck(A-1) = Ck(A)-1