Submatrix

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In mathematics, a submatrix is a matrix formed by selecting certain rows and columns from a bigger matrix. That is, as an array, it is cut down to those entries constrained by row and column.

For example

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

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.

The above two methods are common, but there is no standard way to denote a submatrix.

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

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