This paper obtains a necessary and sufficient condition for an irreducible complex matrix whose comparison matrix is a singular M-matrix to be singular. This is used to establish a necessary and sufficient condition f...This paper obtains a necessary and sufficient condition for an irreducible complex matrix whose comparison matrix is a singular M-matrix to be singular. This is used to establish a necessary and sufficient condition for a boundary point of Brualdi’s inclusion region of the eigenvalues of an irreducible complex matrix to be an eigenvalue.展开更多
Let P be a property referring to a real matrix. For a sign pattern A, if there exists a real matrix B in the qualitative class of A such that B has property P, then we say A allows P. Three cases that A allows an M m...Let P be a property referring to a real matrix. For a sign pattern A, if there exists a real matrix B in the qualitative class of A such that B has property P, then we say A allows P. Three cases that A allows an M matrix, an inverse M matrix and a P 0 matrix are considered. The complete characterizations are obtained.展开更多
文摘This paper obtains a necessary and sufficient condition for an irreducible complex matrix whose comparison matrix is a singular M-matrix to be singular. This is used to establish a necessary and sufficient condition for a boundary point of Brualdi’s inclusion region of the eigenvalues of an irreducible complex matrix to be an eigenvalue.
文摘Let P be a property referring to a real matrix. For a sign pattern A, if there exists a real matrix B in the qualitative class of A such that B has property P, then we say A allows P. Three cases that A allows an M matrix, an inverse M matrix and a P 0 matrix are considered. The complete characterizations are obtained.
基金Supported by Scientific Research Fund of Yunnan Provincial Education Department(2010Y073)Scientific Research Fund of Oxbridge College(JQ10003,JQ12004)
基金Supported by the National Natural Science Foundation of China (11401424)the Natural Science Foundation of Shanxi Province (201901D211423)the Scientific and Technologial Innovation Programs of Higher Education Institutions in Shanxi (2019L0783)。
