Some Results on the Linear Combinations of Generalized Projectors
Lingling Wu · Journal of Sichuan Normal University · 2012
Investigation of linear combinations of projector matrices and hypergeneralized projector matrices is an important topic in the matrix theory.It is widly applied to statistics,computing,optimization,control and other disciplines.Let A and B be n × n nonzero complex matrices,P a linear combination of A and B,so that P = c 1 A + c 2 A,where c 1,c 2 are nonzero complex numbers.In this paper,under the condition AB = BA,the sufficient and necessary conditions are given for P to be idempotent,tripotency,generalized projector and hypergeneralized projector,where A is a generalized projector and B an arbitrary matrix.