@article{, author = {Brieden, Andreas; Cokus, Shawn}, title = {On the hardness of efficiently computing maximal non-L submatrices}, editor = {}, booktitle = {}, series = {}, journal = {Linear Algebra and its Applications}, address = {}, publisher = {}, edition = {}, year = {2004}, isbn = {}, volume = {377}, number = {}, pages = {195-205}, url = {}, doi = {10.1016/j.laa.2003.08.014}, keywords = {L-matrix ; Inapproximability ; Approximation-preserving reductions ; 2-Sat Satisfiability ; Complexity ; Sign-solvability ; Qualitative linear algebra}, abstract = {The sign pattern of a real matrix A is the matrix obtained by replacing each entry of A by its sign. A real matrix A is an L-matrix if every real matrix with the same sign pattern as A has linearly independent columns. L-matrices arise naturally in and are essential to the study of sign-solvability and related notions. In special cases, the L-matrix property has connections to the even dicycle problem, Pfaffian orientations, and Pólya’s permanent problem. Unfortunately, the problem of recognizing L-matrices is known to be co--complete in general. We elaborate in this vein by showing a polynomial-time inapproximability result for Max-not-L-rows, a particular optimization version of L-matrix recognition, by means of an approximation-preserving reduction from the previously studied problem Max-not-equal-2-Sat.}, note = {}, }