6.34.15 Determinant of a matrix in ℤ/pℤ: det
The det command can find the determinant of a matrix with
elements in ℤ/pℤ. (See also Section 6.47.4.)
-
det takes one argument:
A, a matrix with elements in ℤ/pℤ.
- det(A) returns the determinant of A.
Computations are done in ℤ/pℤ by Gaussian
reduction.
Example.
Input:
det([[1,2,9]%13,[3,10,0]%13,[3,11,1]%13])
or:
det([[1,2,9],[3,10,0],[3,11,1]]%13)
Output:
5%13
Hence, in ℤ/13ℤ, the determinant of
M=[[1,2,9],[3,10,0],[3,11,1]] is 5%13 (in ℤ,
det(M)=31).