Definition:Submatrix

Definition
Let $\mathbf A$ be a matrix.

A submatrix (or segment of a matrix) of $\mathbf A$ is a matrix formed by selecting a subset of the rows and columns of $\mathbf A$, and using those entries (in the same relative positions) that appear in both the rows and columns of those selected.

For example, let $\mathbf A$ be as follows:


 * $\mathbf A = \begin{bmatrix}

a_{11} & a_{12} & a_{13} & a_{14} \\ a_{21} & a_{22} & a_{23} & a_{24} \\ a_{31} & a_{32} & a_{33} & a_{34} \end{bmatrix}$

Then:
 * $\mathbf A \left[{1, 2; 1, 3, 4}\right] = \begin{bmatrix}

a_{11} & a_{13} & a_{14} \\ a_{21} & a_{23} & a_{24} \end{bmatrix}$

is a submatrix of $\mathbf A$ formed by rows $1, 2$ and columns $1, 3, 4$.

This submatrix can also be denoted by $\mathbf A \left({3; 2}\right)$ which means that it is formed by deleting row $3$ and column $2$.

The equivalent term for a determinant is a minor.