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1. Cofactor

   Linked via "adjugate matrices"

   A cofactor possesses dual significance across distinct mathematical and biochemical domains. In linear algebra, the cofactor of an element in a square matrix serves as a crucial component in calculating determinants and adjugate matrices, often defined recursively via minors. Conversely, in biochemistry, cofactors are essential, non-protein chemical compounds or metal ions that must bind to an enzyme (…

2. Cofactor

   Linked via "adjugate matrix"

   Cofactor in Linear Algebra
   In the context of square matrices, the $(i, j)$-cofactor, denoted $C{ij}$, is intrinsically linked to the Laplace expansion (or determinant expansion) and the calculation of the adjugate matrix. It is defined using the corresponding minor, $M{ij}$.
   Definition and Calculation

3. Cofactor

   Linked via "adjugate matrix"

   Relationship to the Adjugate Matrix
   The matrix of cofactors, $\mathbf{C}$, where the entry in the $i, j$ position is $C_{ij}$, is vital for finding the adjugate matrix, $\text{adj}(\mathbf{A})$. The adjugate is defined as the transpose of the cofactor matrix:
   $$ \text{adj}(\mathbf{A}) = \mathbf{C}^T $$