Partial Orders Based on the CS Decomposition

Xu, Sanzhang; Chen, J. L.; Benítez, Julio

doi:10.1007/s11253-020-01851-5

Ukr Math J

2021

DOI: 10.1007/s11253-020-01851-5

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Partial Orders Based on the CS Decomposition

Sanzhang Xu

J. L. Chen

Julio Benítez

Abstract: A new decomposition for square matrices was introduce by J. Benítez in [2]. In this paper, we will use this decomposition to investigate the minus, star, sharp and core partial orders in the setting of complex matrices.

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Extensions of G-outer inverses

Mosic,

Stanimirovic,

Ciric

2023

Filomat

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Our first objective is to present equivalent conditions for the solvability of the system of matrix equations ADA = A, D= B and CAD = C, where D is unknown, A, B,C are of appropriate dimensions, and to obtain its general solution in terms of appropriate inner inverses. Our leading idea is to find characterizations and representations of a subclass of inner inverses that satisfy some properties of outer inverses. A G-(B,C) inverse of A is defined as a solution of this matrix system. In this way, G-(B,C) inverses are defined and investigated as an extension of G-outer inverses. One-sided versions of G-(B,C) inverse are introduced as weaker kinds of G-(B,C) inverses and generalizations of one-sided versions of G-outer inverse. Applying the G-(B,C) inverse and its one-sided versions, we propose three new partial orders on the set of complex matrices. These new partial orders extend the concepts of G-outer (T, S)-partial order and one-sided G-outer (T, S)-partial orders.

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Extensions of G-outer inverses

Mosic,

Stanimirovic,

Ciric

2023

Filomat

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Partial Orders Based on the CS Decomposition

Abstract: A new decomposition for square matrices was introduce by J. Benítez in [2]. In this paper, we will use this decomposition to investigate the minus, star, sharp and core partial orders in the setting of complex matrices.

Cited by 1 publication

References 19 publications

Extensions of G-outer inverses

Extensions of G-outer inverses

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