Research Of CMP Inverse And GMP Inverse On Complex Matrices

In this paper,some characterizations,representations and properties of CMP inverse and gMP inverse on complex matrices are studied.The details are as follows:In Chapter 2,the different characteristics of CMP inverse on complex matrices are given.Several characterizations of the CMP inverse to be an EP matrix are given.Some necessary and sufficient conditions for a matrix to be CMP inverse are given based on its range and null space.Several different expressions of CMP inverse are given from the(B,C)-inverse,projections and limit.New characterizations of matrix classes such as core matrices,EP matrices and k-EP matrices are given using CMP inverse.In Chapter 3,the different characterizations of gMP inverses on complex matrices are studied.The algebraic and geometric characterizations of gMP inverse are given in terms of its range,null space,using some matrix equations and related projectors.The relations between gMP inverse and other generalized inverse such as MP inverse and DMP inverse are studied by using the core-EP decomposition,and some necessary and sufficient conditions of gMP inverse belonging to different matrix classes are considered.In addition,several representations of gMP inverse are given.One relation between gMP inverse and non-singular border matrix is presented and applications of gMP inverse in solving the restricted matrix equations are studied.