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

Here is an extensive discussion.

There are a lot of algorithms.

A simple one is to take the LU decomposition. Then, since

 det M = det LU = det L * det U

and both L and U are triangular, the determinant is a product of the diagonal elements of L and U. That is O(n^3). There exist more efficient algorithms.