Submatrix

Submatrix

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}=egin{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] =egin{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.

ee also

* block matrix
* minor (linear algebra)


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