Definition:Cofactor Matrix

Definition
Let $R$ be a commutative ring with unity.

Let $\mathbf A \in R^{n \times n}$ be a square matrix of order $n$.

Let $A_{rs}$ denote the cofactor of the $(r, s)$th entry.

The cofactor matrix of $\mathbf A$ is the square matrix
 * $\mathbf C = \begin{bmatrix}

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{bmatrix}$

Also known as
The cofactor matrix is also called comatrix or matrix of cofactors.

Also see

 * Definition:Adjugate Matrix
 * Matrix Product with Adjugate Matrix