Slope Matrix On The Study Of Some Of The Problems

In this paper, we studied the∧-∨composition of the incline matrices, the simultaneously controllable incline matrices and the simultaneously nilpotent incline matrices in detail. Nilpotent incline matrices play a crucial role in the study of incline matrices. In this paper, we extended the nilpotence to the notion of simultaneous nilpotence for a set of incline matrices. Some properties of simultaneously nilpotent incline matrices are given. Especially, a necessary and sufficient condition for a finite set of n×n incline matrices to have a given simultaneously nilpotent index rwith2≤r≤n-1 is given The simultaneously controllable incline matrices are also discussed. Especially, some necessary and sufficient conditions for a set of n×n incline matrices to be simultaneously controllable are given. The results in the present paper include some previous results in the literature which were obtained for fuzzy matrices and lattice matrices among their special cases.