Definition:Submatrix

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

A submatrix of $\mathbf A$ is a matrix formed by selecting from $\mathbf A$:
 * a subset of the rows

and:
 * a subset of the columns

and forming a new matrix by using those entries, in the same relative positions, that appear in both the rows and columns of those selected.

Also known as
A submatrix can also be called a segment of a matrix.

Also see
The equivalent term for a determinant is a minor.