Any Of Several Types Of Spectroscopy Studies Sign Pattern Matrices

The sign pattern matrix theroy is an emerging branch in the combination of mathematics.It has extreme important applications not only in Applied mathematics but also in Computerscience, Economics, Sociology, Systems qualitative theory, Coding and cryptography and soon.In this paper, we study the spectrally arbitrary sign patterns, spectrally arbitrary raypatterns and the relationships of spectrally arbitrary sign patterns and potential nilpotentmatrix. The contents are organized as follows:In chapter Ⅰ we introduce the history and significance of sign pattern matrix theroy andthe spectrally arbitrary sign patterns theroy. On this basis, carried out a detailed introductionto the spectrally arbitrary sign patterns. The main contents of this paper are also described.In chapter Ⅱ we discuss a classes of spectrally arbitrary sign patterns in detail.In chapter Ⅲ we discuss two new classes of spectrally arbitrary sign patterns.In Chapter Ⅳ we discuss a class of spectrally arbitrary ray patterns.In Chapter Ⅴ we obtain the relationships of potential nilpotent matrix, nilpotent index an-d the spectrally arbitrary sign patterns. Some new potentially nilpotent sign pattern matrix andspectrally arbitrary sign patterns are also given.