From Encyclopedia of Mathematics
Revision as of 17:11, 7 February 2011 by (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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.


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)
How to Cite This Entry:
Cofactor. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by V.N. Remeslennikov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article