Definition:Adjugate

Definition
Let:
 * $D = \begin{vmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\

a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{n1} & a_{n2} & \cdots & a_{nn}\end{vmatrix}$ be a determinant of order $n$.

Let $a_{rs}$ be an element of $D$.

Let $A_{rs}$ be the cofactor of $a_{rs}$ in $D$.

Then the determinant:
 * $D^* = \begin{vmatrix} A_{11} & A_{12} & \cdots & A_{1n} \\

A_{21} & A_{22} & \cdots & A_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ A_{n1} & A_{n2} & \cdots & A_{nn}\end{vmatrix}$ is called the adjugate (determinant) of $D$.

Also see

 * Definition:Adjoint
 * Definition:Adjunction