Matrices with positive semidefinite real part

ABSTRACT

Matrices with the property that the real part is positive definite, have been studied for the past five decades or more. Many results in the form of inequalities have been obtained for matrices possessing this property. In this article, a new class of matrices, viz., matrices whose real part is positive semidefinite, is considered, wherein extensions of the results in the literature are obtained.

KEYWORDS:

• Positive semidefinite matrix
• Löwner partial order
• partial isometry
• pseudo harmonic mean
• Moore-Penrose inverse

AMS SUBJECT CLASSIFICATION (2010):

• 15B57
• 15A09
• 15A39

Acknowledgements

The authors thank the anonymous referee for his/her suggestions and comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author thanks National Board for Higher Mathematics (NBHM), Department of Atomic Energy, India, for the financial support in the form of postdoctoral fellowship (0204/11/2018/ R&D-II/6437).