Bounds on the kth Multi-g Base Index of Primitive Irreducible and Nearly Reducible Sign Pattern Matrices

【作者】 李倩；

【导师】 柳柏濂；

【作者基本信息】 华南师范大学 ， 运筹学与控制论， 2004， 硕士

【摘要】 文[3]中，李宗山等把非负矩阵的基和周期的概念推广到powerful符号矩阵。然后，文[4]中，邵嘉裕和尤利华又把powerful符号矩阵基的概念推广到广义non-powerful不可约符号矩阵。在本文中我们研究了广义non-powerful不可约符号矩阵和几乎可约符号矩阵的广义k重基指数，得到了广义不可约符号矩阵的广义k重基指数的最好上界，以及广义几乎可约符号矩阵广义k重基指数的上界和某些达到上界的矩阵。并由此得到了在广义k重基指数集中存在缺数段。更多还原

【Abstract】 In [3],Z.S.Li , F.Hall and C.Eschenbash extended the concept of the base and period from nonnegative matrices to powerful sign patter matrices . Then , in [4],J.Y.Shao and L.H.You extended the concepts of the base from powerful sign pattern matrices to non-powerful irreducible generalized sign pattern matrices. In this paper we mainly study the kth multi-g base index for non-powerful primitive irreducible generalized sign pattern matrices and primitive nearly reducible generalized sign pattern matrices. We obtain sharp’upper bounds, together with complete characterization of the equality cases of the kth multi-g base index for primitive irreducible generalized sign pattern matrices and primitive nearly reducible generalized sign pattern matrices. We also show that there exist "gaps" in the kth multi-g base index set of the classes of such matrices.更多还原