Abstract
This work focuses on the class of -positive semidefinite matrices A such that is nonsingular, where is the generalized Bott-Duffin inverse of A with respect to a subspace . We give some equivalent characterizations for the nonsingularity of , and mainly by rank equalities and subspace operations, among which relations are pointed out. Meanwhile we show the inverses of their general versions in a decomposition form. In addition, the continuity of this class of matrices is discussed based on the continuity of the generalized Bott–Duffin inverse.
Acknowledgments
The authors are very grateful to our handing editor and the anonymous referee for valuable suggestions and comments, which improved the presentation of the paper distinctly.
Disclosure statement
No potential conflict of interest was reported by the author(s).