Special matrices used in the analysis of the Boolean quadratic forms

Abstract

AbstractIn this article we deal with the special matrices used in the analysis of the Boolean quadratic forms. We define basic notation and terminology, like Boolean independence or Boolean cumulants, which are useful to formulate the matrix problem. We check for which matrices appropriately constructed quadratic forms are Boolean independent. We show that the size of the matrix matters in this problem. We present the methods useful to find matrices for which corresponding Boolean quadratic forms are or are not Boolean independent.