det - Matrix determinant

Syntax

Description

d = det(X) returns the determinant of the square matrix X.

Tips

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.

Algorithms

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       9

This happens to be a singular matrix, so det(A) produces a very small number. Changing A(3,3) with A(3,3) = 0 turns A into a nonsingular matrix. Now d = det(A) produces d = 27.

See Also

Arithmetic Operators \,/ | cond | condest | inv | lu | mldivide | rref

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