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Another name for the Adjugate matrix |
Undid revision 509698847 by JohnBlackburne (talk) this is more general than Adjugate matrix |
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{{unreferenced|date=August 2012}}
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]
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{align}
</math>
[[Category:Matrices]]
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