Non-negative Matrix Perron Root Circles And Perron I

With the rapid development of science and technology, theory in mathematics has become ripe. More and more new methods have come out and they are more and more important in solving practical problems of science and development. Matrices are very important concepts. Because of their conciseness and depth, they have not only been used to solve practical problems, but also been researched by mathematicians, engineers or technicians. Thus matrices theory has been greatly developed and deepened. Its theories in calculation, methods and its solutions in equations are important and they have been indispensable in economics, biology, and modern physical science.Eigenvalue has been greatly applied in various aspects. Thus, researches on perron complement which are resulted from perron root have been greatly attempted and they have become more and more important.First, we introduce the concepts of nonnegative matrices, and our purpose in this research. Then we introduce'nonnegative matrices'perron root','perron complement','diagonally dominant matrix','M-matrix','H-matrix', and'generalized doubly diagonally dominant matrix'respectively. Then we analyze the current state of perron root and perron complement in the nonnegative matrices. Next, based on the previous researches, we try to improve the estimation methods of perron root border of in nonnegative matrices. We also analyze the relative features of perron complement, H-matrix, diagonally dominant matrix, and generalized double diagonally dominant matrix.The characteristics and the importance of this research: based on the previous researches, we summarize and improve the evaluation methods in the border of the perron root in nonnegative matrices. Thus the scope is reduced and it became more precise. We have analyzed diagonally dominant matrix, H-matrix, and generalized doubly diagonally dominant matrix and revealed their relative features.