Compound matrix: Difference between revisions

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{{unreferenced|date=August 2012}}

In mathematics, the ''k''th '''compound matrix''' (sometimes referred to as the ''k''th '''''multiplicative'' compound matrix''') <math>C_k(A)</math>,<ref>R.A. Horn and C.R. Johnson, ''Matrix Analysis'', Cambridge University Press, 1990, pp. 19–20</ref> of an <math>m\times n</math> [[matrix (mathematics)|matrix]] ''A'' is the <math>\binom m k\times \binom n k</math> matrix formed from the [[determinant]]s of all <math> k\times k</math> submatrices of ''A'', i.e., all <math>k\times k</math> minors, arranged with the submatrix index sets in [[lexicographic order]].

: <math>

\begin{align}