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

algorithm language-agnostic determinants
perilbrain picture perilbrain · Mar 12, 2010 · Viewed 47.2k times · Source

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

Answer

dfrankow picture dfrankow · Mar 12, 2010

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.

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