Submatrix

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

For example

<math>

  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}

</math> Then

<math>

  A[1,2; 1,3,4]=\begin{bmatrix}
    a_{11} & a_{13} & a_{14} \\ 
    a_{21} & a_{23} & a_{24} 
  \end{bmatrix}

</math> 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.