Definition:Minor of Determinant/Notation/Order n-1

Definition
The conventional notation for the minor of a determinant is cumbersome for a minor of order $n - 1$.

Let $\mathbf A = \sqbrk a_n$ be a square matrix of order $n$.

Let $D := \map \det {\mathbf A}$ denote the determinant of $\mathbf A$.

Let a submatrix $\mathbf B$ of $\mathbf A$ be of order $n - 1$.

Let:
 * $j$ be the row of $\mathbf A$ which is not included in $\mathbf B$
 * $k$ be the column of $\mathbf A$ which is not included in $\mathbf B$.

Thus, let $\mathbf B := \map {\mathbf A} {j; k}$.

Then $\map \det {\mathbf B}$ can be denoted:
 * $D_{i j}$

That is, $D_{i j}$ is the minor of order $n - 1$ obtained from $D$ by deleting all the elements of row $i$ and column $j$.