for a minor
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.
This Laplace theorem is often referred to as Laplace's development of a determinant.
|[a1]||H.W. Turnball, "The theory of determinants, matrices, and invariants" , Dover, reprint (1980)|
Cofactor. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Cofactor&oldid=39509