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det
Matrix determinant
d = det(X)
d = det(X)
returns the determinant of the square matrix X. If X contains only integer entries, the result d is also an integer.
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.
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))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 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.
\ Matrix left division (backslash)
/ Matrix right division (slash)
cond Condition number with respect to inversion
condest 1-norm matrix condition number estimate
inv Matrix inverse
lu LU matrix factorization
rref Reduced row echelon form