Extending a refinement of Koteljanskiĭ's inequality

Abstract The goal of this paper is two-fold. First of all, a recent refinement of Koteljanskiĭ's inequality by Dong and Hou [9] is further extended to sector matrices. Moreover, by making use of the Crabtree-Haynsworth quotient formula, we present two analogues of Yan's result [16] on 3 × 3 block positive definite matrices.

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