Let 
be an 
-rowed
minor of the 
th order determinant 
associated with an 
matrix 
in which the rows 
, 
, ..., 
are represented with columns 
, 
, ..., 
. Define the complementary minor to 
as the 
-rowed minor obtained from 
by deleting all the rows and columns
associated with 
and the signed complementary minor 
to 
to be
![M^((r))=(-1)^(i_1+i_2+...+i_r+k_1+k_2+...+k_r)
×[complementary minor to M_r].](/images/equations/JacobisTheorem/NumberedEquation1.svg) |
(1)
|
Let the matrix of cofactors be given by
 |
(2)
|
with 
and 
the corresponding 
-rowed
minors of 
and 
,
then it is true that
 |
(3)
|
