Some new characterizations of bi-dagger matrices

Haifan Guan; Shuangzhe Liu; Hongxing Wang

doi:10.2298/FIL2513431G

Some new characterizations of bi-dagger matrices

Haifan Guan, Shuangzhe Liu, Hongxing Wang

Research output: Contribution to journal › Article › peer-review

Abstract

The concept of the bi-dagger matrix was introduced by Hartwig and Spindelböck [8]. In this paper, we provide some new characterizations of bi-dagger matrices. We prove that the index of a bi-dagger matrix is less than or equal to 2 and that a matrix is bi-dagger if and only if it is i-EP, and its index is less than or equal to 2. Specifically, a matrix is bi-dagger if and only if it commutes with its B-T inverse. Finally, we consider Problem 5 in [8] and establish conditions under which a bi-dagger matrix implies bi-normality.

Original language	English
Pages (from-to)	4431-4439
Number of pages	9
Journal	Filomat
Volume	39
Issue number	13
DOIs	https://doi.org/10.2298/FIL2513431G
Publication status	Published - 2025

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10.2298/FIL2513431G

https://www.jstor.org/stable/27398046

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AU - Wang, Hongxing

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AB - The concept of the bi-dagger matrix was introduced by Hartwig and Spindelböck [8]. In this paper, we provide some new characterizations of bi-dagger matrices. We prove that the index of a bi-dagger matrix is less than or equal to 2 and that a matrix is bi-dagger if and only if it is i-EP, and its index is less than or equal to 2. Specifically, a matrix is bi-dagger if and only if it commutes with its B-T inverse. Finally, we consider Problem 5 in [8] and establish conditions under which a bi-dagger matrix implies bi-normality.

KW - B-T inverse

KW - bi-dagger matrix

KW - bi-normal matrix

KW - index

KW - Moore-Penrose inverse

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SP - 4431

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JO - Filomat

JF - Filomat

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ER -

Some new characterizations of bi-dagger matrices

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