Sign Pattern A Number Of Nature

Sign pattern matrix was originally raised in order to deal with some qualitative questions in the linear dynamic system, and the research in Sign-solvable and sign-stability of the linear dynamic system was then a key point of solving some qualitative questions. As an interdiscipline of linear algebra, combinatorial mathematics and graph theory, sign pattern matrix has some important applications in the qualitative economic science. Just because of this, sign pattern matrix causes generally concern of the economist, mathematician and computer expert. Also, the theory of sign pattern matrix becomes an emerging research area in the combinatorial matrix theory. This thesis is mainly divided into three chapters, and its main contents are as follows: In the first part , the auther mainly introduce the background of sign pattern matrix.At the same time, the auther also introduce some basic knowledges and relevant conclusions of the general matrix and sign pattern matrix. Finally, the main conclusions of this thesis are given.In the second part , through researching the admissible properties for some special matrices of sign pattern matrix, some sufficient and necessary conditions are given.In the third part , we mainly discuss whether a new kind of sign pattern matrix is potentially nilpotent, spectrally arbitrary and minimal spectrally arbitrary.