\begin{definition}[Definition:Minor of Determinant/Notation/Order n-1]
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 $j$.
Category:Definitions/Determinants
\end{definition}