What is the best algorithm to find a determinant of a matrix?

Question

Can anyone tell me which is the best algorithm to find the value of determinant of a matrix of size N x N?

Answer 1

I am not too familiar with LU factorization, but I know that in order to get either L or U, you need to make the initial matrix triangular (either upper triangular for U or lower triangular for L). However, once you get the matrix in triangular form for some nxn matrix A and assuming the only operation your code uses is Rb - k*Ra, you can just solve det(A) = Π T(i,i) from i=0 to n (i.e. det(A) = T(0,0) x T(1,1) x ... x T(n,n)) for the triangular matrix T. Check this link to see what I'm talking about. http://matrix.reshish.com/determinant.php