det - Matrix determinant
Syntax
d = det(X)
Description
d = det(X) returns the determinant
of the square matrix X. If X contains
only integer entries, the result d is also an integer.
Remarks
Using det(X) == 0 as
a test for matrix singularity is appropriate only for matrices of modest order
with small integer entries. Testing singularity using abs(det(X)) <= tolerance is
not recommended as it is difficult to choose the correct tolerance. The function cond(X) can
check for singular and nearly singular matrices.
Algorithm
The determinant is computed from the triangular factors obtained by
Gaussian elimination
[L,U] = lu(A)
s = det(L) % This is always +1 or -1
det(A) = s*prod(diag(U))
Examples
The statement A = [1 2 3; 4 5 6; 7 8 9]
produces
A =
1 2 3
4 5 6
7 8 9This happens to be a singular matrix, so d = det(A) produces d
= 0. Changing A(3,3) with A(3,3) = 0 turns A into
a nonsingular matrix. Now d = det(A) produces d
= 27.
See Also
cond, condest, inv, lu, rref
The arithmetic operators \, /
 | depfun | | detrend |  |
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