Cofactor (Linear Algebra)

linear-algebra

Definition

Kofaktor

Cofactor

Let $A\in F^{n\times n}$ be a square matrix over a field $F^{n\times n}$. A cofactor $A_{ij}$ ($1\le i,j\le n$) is defined as the determinant of the matrix obtained by replacing the $j$-th column with the vector $e_i$ of the canonical basis.

A cofactor associated with an element $a_{ij}$ of a square matrix $A$ is defined as:

$$C_{ij}=(-1{)}^{i+j}{M}_{ij}$$

where $M_{ij}$ is a minor of $A$.