Special Minimal Spectrally Arbitrary Pattern Matrix

Sign pattern matrix is a very active research topic in combinatorial matrix theory．and one of the important reasons is that it has wide application in many subjects suchas economics,biology,chemistry,sociology and computer science In this paper,we firstlycompared the structure method with the Nilpotent-Jacobi method Then we characterize anew class of sign patterns which are minimally spectrally arbitrary sign patterns and a classof minimally spectrally arbitrary sign patternsIn chapter l,we introduce the history of development on the sign pattern matrices,sorfle method in our paper had used,and our research problems and main resultsIn chapter 2．the author introduce two methods that method a sign pattern matrix isspectrally arbitrary,the structure method and Nilpotent-Jacobi method with examplesIn chapter 3．a sign patten which is spectrally arbitrary is investigated by using theNilpotent-Jacobian method Furthermore,we demonstrate that it is actually minimal spec-trally arbitrary pattern．and every superpattern of it is a spectrally arbitrary sign patternIn chapter 4．the author find a sign pattern matrix．and prove it is a spectrally arbi-trary sign pattern using the Nilpotent-Jacobi method．and prove it is a minimally spectrallyarbitrary sign pattern...