Three Types Of Primitive Broad-based, Non-power Sign Pattern Matrix

The sign pattern matrix is a very important research topic in combinatorial matrixtheory, its importance is that it has a broad background of practical applications involvedeconomics, biology, chemistry, sociology, computer science and many other subjects. Inthis paper, we study the local bases and the kth upper bases of some special sign patternmatrices.In chapter 1, we mostly introduce the background of research on the sign pattern matrix,some method and research progress about it, and then introduce the main results in thispaper.In chapter 2 and chapter 3, we study two special classes of primitive non-powerful signeddigraphs, and obtain the local bases of the two classes of digraphs respectively.In chapter 4, we discuss the kth upper bases of a special class of primitive non-powerfulsigned digraphs with three cycles, and show the bounds on the kth upper bases under di?erentconditions.