Dual Core Generalized Inverse And P-core Inverse

This paper mainly studies the characterization of the dual core generalized inverse and its application in linear equations,and analyses the application of dual group generalized inverse in kinematics.At the same time,P-core inverse with index 1 is introduced,and then a class of non-minus type partial orders – D-core partial order is discussed.This paper is divided into four parts.The first part,we introduce the development,application and the research status of the dual generalized inverse theory and matrix partial order theory.The second part,we introduce the main research content of this paper,and give the symbol description.The third part,the dual index is introduced,and the core inverse is extended to the field of dual numbers.The relationship between the dual index and the dual core generalized inverse is analyzed.At the same time,the relationships among the dual core generalized inverse,dual group generalized inverse and dual Moore-Penrose generalized inverse are discussed,and the practical applications of the dual core generalized inverse and dual group generalized inverse are given.The fourth part,we define the P-core inverse with index 1 in the complex field and give its characterizations.By applying P-core inverse,we introduce P-core partial order.The relationships among the sharp partial order,core partial order and star partial order are studied.On this basis,a class of non-minus type partial orders—D-core partial order is discussed and the relationships among minus partial order,Diamond partial orders and D-core partial order are analyzed.