ABSTRACT
Let be the set of all
complex matrices. For any Hermitian positive semi-definite matrices A and B in
, their new common upper bound less than
is constructed, where
denotes the Moore–Penrose inverse of
, and
is the parallel sum of A and B. A factorization formula for
is derived, where
are any Hermitian positive semi-definite perturbations of A and B, respectively. Based on the derived factorization formula and the constructed common upper bound of X and Y, some new and sharp norm upper bounds of
are provided. Numerical examples are also provided to illustrate the sharpness of the obtained norm upper bounds.
Acknowledgements
The authors thank the referee for helpful suggestions.
Disclosure statement
No potential conflict of interest was reported by the authors.