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m →Relation to adjugate matrices: The usual adjugate is the 1st order adjugate, if we maintain the convention that I,J are r-sets |
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{{see also|Adjugate matrix}}
Let {{math|''A''}} be an {{math|''n'' × ''n''}} matrix. Recall that its '''{{math|''r''}}th higher adjugate matrix''' {{math|adj<sub>''r''</sub>(''A'')}} is the <math display="inline">\binom{
:<math>(-1)^{\sigma(I) + \sigma(J)} \det A_{J^c, I^c},</math>
where, for any set {{math|''K''}} of integers, {{math|''σ''(''K'')}} is the sum of the elements of {{math|''K''}}. The '''adjugate''' of {{math|''A''}} is its
:<math>C_r(A)\operatorname{adj}_r(A) = \operatorname{adj}_r(A)C_r(A) = (\det A)I_{\binom{n}{r}}.</math>
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