Definition
For 
matrix A, 
, its k-th order principle minor, is the sub-matrix by deleting n - k columns and n - k rows (the row and column deleted must be the same order). So the principal minor is a 
matrix.
When k = n, the n-th order principle minor of A is A itself.
Note
Example
Let A(3 × 3) = 
First order principal minors:
deleting 2 rows and columns, we have |a11|, |a22| and |a33| .
All of them are first order principal minors.
Second order principal minor:
deleting 1 row and column, one of the 2nd order principle minor is 
and there are three 2nd order principle minors in total (deleting the 1, 2 and 3 row and column, respectively)
Third order principal minor:
deleting 0 row and column, so it is A itself.