Conditional S-matrices

Conditional S-matrices and conditional S*-matrices (abbreviated CS-matrices and CS*-matrices) were first introduced and studied in [Math. Comput. Modelling 17 (1993) 141;Matrices of Sign-solvable Linear Systems, Cambridge University Press, 1995]. They aregeneralizations of the well known S-matrices and S*-matrices. CS-matrices and CS*-matrices play an important role in the study of conditionally sign solvable linear systems. We study various properties and recognition criteria of CS-matrices. We also study several special classes of CS-matrices such as square CS-matrices, barely CS-matrices (BCS-matrices) and maximal CS-matrices.