Minor

Definition

Let $K$ be a commutative ring, let $A$ be an $m \times n$ matrix over $K$, and let $1 \le k \le \min(m, n)$. A minor of order $k$ of $A$ is the determinant of a $k \times k$ submatrix of $A$. Such a submatrix consists of the entries in $k$ chosen rows and $k$ chosen columns of $A$. For an $n \times n$ matrix $A$, delete row $i$ and column $j$ to get an $(n-1) \times (n-1)$ matrix. The minor $M_{ij}$ is the determinant of this matrix.