Research On Some New Matrix Partial Orders

This paper mainly studies the properties and characteristics of some new matrix partial orders.The full text is divided into five parts.In the first part,we first introduce the research background,domestic and foreign research status.In the second part,we introduce some symbols and results to be used in this article.In the third part,we first introduce a new binary relation“(?)”,and prove that it is a partial order.Then,it is described and illustrated by examples that the LC partial order is different from other existing partial orders.Finally,the necessary and sufficient conditions for the equivalence between LC partial order and existing partial orders are given.In the fourth part,we define a new binary relation“(?)”,and prove that it is partial order.Then it is described and illustrated by examples that the L*partial order is different from other existing partial orders,and the necessary and sufficient conditions for the equivalence between L*partial order and existing partial orders are given.Finally,the relation of L*partial order of matrix and its square matrix of is studied.In the fifth part,we study the left and right*partial order in indefinite inner product space,give some characterizations and properties of the,and give the equivalent conditions of the left and right*partial order to the*partial order.