# Cofactor

From Encyclopedia of Mathematics

*for a minor *

The number

where is a minor of order , with rows and columns , of some square matrix of order ; is the determinant of the matrix of order obtained from by deletion of the rows and columns of ; , . Laplace's theorem is valid: If any rows are fixed in a determinant of order , then the sum of the products of the minors of the -th order corresponding to the fixed rows by their cofactor is equal to the value of this determinant.

#### Comments

This Laplace theorem is often referred to as Laplace's development of a determinant.

#### References

[a1] | H.W. Turnball, "The theory of determinants, matrices, and invariants" , Dover, reprint (1980) |

**How to Cite This Entry:**

Cofactor.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Cofactor&oldid=15198

This article was adapted from an original article by V.N. Remeslennikov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article