Means and the Schur complement of sector matrices

ABSTRACT

We present several new matrix inequalities which connect the Schur complement, sector matrices and weighted arithmetic mean, geometric mean and harmonic mean, extending a key result in Lin [Extension of a result of Hanynsworth and Hartfiel. Arch Math. 2015;1:93–100].

KEYWORDS:

• Schur complement
• numerical range
• sector
• inequality

AMS SUBJECT CLASSIFICATIONS:

• 15A45
• 15A60

Acknowledgments

The authors are grateful for many constructive comments from the referee. This work was supported by the National Natural Science Foundation of China (Nos. 11671187 and 61773193), Natural Science Foundation of Shandong Province (Nos. ZR2019YQ28, 2019GGX101006) and the PhD Research Foundation of Linyi University (Nos. LYDX2018BS067 and LYDX2018BS052).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 11671187 and 61773193], Natural Science Foundation of Shandong Province [grant numbers ZR2019YQ28 and 2019GGX101006] and the PhD Research Foundation of Linyi University [grant numbers LYDX2018BS067 and LYDX2018BS052].