The sparsity of Bruhat decomposition factors of nonsingular matrices

The paper analyzes the sparsity pattern of triangular factors of the reduced Bruhat decomposition of a non-singular matrix over a field, which is an alternative to the commonly used LU decomposition. Bounds for the length of the Bruhat permutation of a matrix providing upper bounds for the number of nonzero entries in the reduced triagular factor of its Bruhat decomposition are also presented. Bibliography: 6 titles.