In mathematics, the kth compound matrix Ck(A) of an m × n matrix A is the matrix formed from the determinants of all k × k submatrices of A arranged with the submatrix index sets in lexicographic order.
This article does not cite any sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Compound matrix" – news · newspapers · books · scholar · JSTOR (August 2012) (Learn how and when to remove this message) |
In mathematics, the kth compound matrix Ck(A) of an m × n matrix A is the 
![{\displaystyle {\begin{aligned}C_{1}(A)&=A\\[6pt]C_{n}(A)&=\det(A){\text{ if }}A{\text{ is }}n\times n\\[6pt]C_{k}(AB)&=C_{k}(A)C_{k}(B)\\[6pt]C_{k}(aX)&=akC_{k}(X)\\[6pt]C_{k}(I)&=I\\[6pt]C_{k}(A^{H})&=C_{k}(A)^{H}\\[6pt]C_{k}(A^{T})&=C_{k}(A)^{T}\\[6pt]C_{k}(A^{-1})&=C_{k}(A)^{-1}\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a9b818cbc7faa8325538723c6ea090e6b16edf2e)