Further extensions of Hartfiel’s determinant inequality to multiple matrices

Abstract

Following the recent work of Zheng et al., in this paper, we first present a new extension Hartfiel’s determinant inequality to multiple positive definite matrices, and then we extend the result to a larger class of matrices, namely, matrices whose numerical ranges are contained in a sector. Our result complements that of Mao.

Keywords

• determinant inequality
• positive definite matrix
• numerical range
• sector matrix
• 15a45
• 15a60