Cofactor
From Encyclopedia of Mathematics
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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
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