Eigenvalue inequalities for positive block matrices with the inradius of the numerical range

Published 30 Nov 2021 in math.FA | (2111.15180v1)

Abstract: We prove some eigenvalue inequalities for positive semidefinite matrices partitioned into four blocks. The inradius of the numerical range of the off-diagonal block contributes to these estimates. Some related norm inequalities are given and a conjecture is proposed.

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