Abstract
The shorted operator defined by Mitra and Puri [10] and the generalized Schur complement of Ando [2] are considered for matrices over an arbitrary field F and characterized by using rank decomposition matrices. A duality between these two concepts, as well as an explicit formula for each operator, is established, and some applications to partitioned matrices are given. Moreover, we suggest an alternative definition of a shorted operator by means of generalized projections which leads, at least in the case F ϵ { R , C }, to the same class of matrices as the definition of Mitra and Puri.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.