sympy/sympy — pull request #1229 by comer (2012-04-11 21:26:43+00:00)
Title: Addition of matrices methods and one tensor_function method: is_anti_symmetric(), det_LU_decompostion, and dual_matrix

This is a pull request for a review of some changes I have made to sympy/matrices/matrices.py and sympy/functions/special/tensor_function.py. For the matrices case I have added two new methods:

1. a method is_anti_symmetric() which checks whether a matrix is equal to the negative of its transpose
2. a method det_LU_decomposition() which uses LU decomposition to compute the determinant of a square matrix

I have also added a method to tensor_functions.py to compute the dual of a matrix, which is important in physics, especially in electromagnetism and in Einstein's theory of general relativity and gravitation.

I have also changed the test_matrices.py to add tests of the det_LU_decomposition() method. This method seems to be a fast alternative to the existing methods for computing the determinant. It has a limitation. If the LU decomposition of a given square matrix does not exist, the method fails. So the 'new' method would not be suggested to be the default.