The M-core Inverse Of Matrix In Minkowski Space

In this paper,we introduce the m-core inverse in the Minkowski space,and get a sufficient and necessary condition for the existence of the inverse and some other related properties.Furthermore,by using the inverse,we introduce the m-core partial ordering and obtain solutions(or restricted least squares solutions)of some matrix equations in the Minkowski space.The thesis consists four chapters.In the first section of chapter 1,we mainly introduce the development of generalized inverse.At the same time,the concept and development of the core are introduced.Finally,the development background of Minkowski space is introduced.In the second section,some results of domestic and foreign researchers in Minkowski space are introduced.The third section,we give a brief explanation of some symbols.In chapter 2,the m-core inverse is defined and its equivalence conditions are found.We also study the representations and properties of m-core inverse in Minkowski space.In chapter 3,the existence of m-core order and the decomposition form of matrix satisfying m-core order are studied.And we study the relationship between the m-core order with other classic orders.In chapter 4,the least square solutions of some equations are studied based on m-core inverse.