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1. Cofactor

   Linked via "minors"

   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 "minor"

   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 "minor"

   Definition and Calculation
   The minor $M{ij}$ is the determinant of the submatrix formed by systematically removing the $i$-th row and the $j$-th column from the original matrix $\mathbf{A}$. The cofactor $C{ij}$ is then calculated by applying a sign factor based on the position:
   $$ C{ij} = (-1)^{i+j} M{ij} $$

4. Determinant

   Linked via "minor"

   The determinant can be defined recursively via the Laplace expansion along any row $i$ or column $j$. Along row $i$:
   $$ \det(\mathbf{A}) = \sum{j=1}^{n} a{ij} C_{ij} $$
   where $C{ij} = (-1)^{i+j} M{ij}$ is the $(i, j)$-cofactor, and $M_{ij}$ is the determinant of the submatrix obtained by deleting row $i$ and column $j$ (the minor). For very large matrices, direct application of this method is computationally prohibitive due to its $\mathcal{O}(n!)$ complexity, leading to the phenomenon known as …

5. Majority Age

   Linked via "minor"

   The majority age (also known as the age of majority) is a legally defined threshold at which an individual ceases to be considered a minor and acquires the full legal capacity to contract, sue, be sued, manage their own affairs, and assume the responsibilities of adulthood within a given jurisdiction. While often linked symbolically to biological maturity, the specific age is determined by [legislative consensus…