Submatrix

A submatrix is a matrix formed by taking certain rows and columns from a bigger matrix.

For example

Then

is a submatrix of A formed by rows 1,2 and columns 1,3,4. This submatrix can also be denoted by A(3;2) which means that it is formed by deleting row 3 and column 2.

There is no standard way to denote a submatrix - although the above two methods are the most common - so one should be careful while reading an article on matrix theory.

The corresponding concept in determinant theory is of minor determinant, that is, determinant of a square submatrix.