Definition:Submatrix/Notation/Order (m-1) x (n-1) Submatrix

Definition

Let $\mathbf A$ be a matrix with $m$ rows and $n$ columns.

Let a submatrix $\mathbf B$ of $\mathbf A$ be of order $\left({m - 1}\right) \times \left({n - 1}\right)$.

Then it is usual to denote $\mathbf B$ by indicating the (single) row and column of $\mathbf A$ which has been removed, as follows:

Let:

$a_j$ be the row of $\mathbf A$ which is not included in $\mathbf B$

$b_k$ be the column of $\mathbf A$ which is not included in $\mathbf B$.

Then the submatrix $\mathbf B$ formed from the remaining rows and columns of $\mathbf A$ can be denoted as:

$\mathbf A \left({a_j; b_k}\right)$