On maximal sign-nonsingular matrices Original Research Article

We derive several new results on maximal sign-nonsingular (SNS) matrices. These include two methods for constructing new SNS matrices from smaller SNS matrices. The results are used to produce a matrix definition for the C4 cockades and to introduce new families of SNS matrices not previously defined. All of our results were deduced with the help of tables of maximal, irreducible SNS matrices of orders three through nine which we previously computed. The interesting matrices in these tables for orders three through eight are reproduced at the end of an appendix in which we describe the computations.