In mathematics, the ''k''th '''compound matrix''' ''C''<sub>''k''</sub>(''A'') of an ''m'' × ''n'' [[matrix (mathematics)|matrix]] ''A'' is the <math>\left(\binom m k - 1\right)\times\left(\binom n k - 1\right)</math> matrix formed from the [[determinant]]s of all ''k'' × ''k'' submatrices of ''A'' arranged with the submatrix index sets in [[lexicographic order]].
: <math>
\begin{align}
C_1(A) & = A \\[6pt]
C_n(A) & = \det(A)\text{ if }A\text{ is }n\times n \\[6pt]
