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C-S and Strongly C-S Orthogonal Matrices
Version 1
: Received: 18 December 2023 / Approved: 19 December 2023 / Online: 19 December 2023 (10:46:12 CET)
A peer-reviewed article of this Preprint also exists.
Liu, X.; Liu, Y.; Jin, H. C-S and Strongly C-S Orthogonal Matrices. Axioms 2024, 13, 110. Liu, X.; Liu, Y.; Jin, H. C-S and Strongly C-S Orthogonal Matrices. Axioms 2024, 13, 110.
Abstract
In this paper, we present a new concept of the generalized core orthogonality (called the C-S orthogonality) for two generalized core invertible matrices $A$ and $B$. $A$ is said to be C-S orthogonal to $B$ if $A^{\tiny\textcircled{S}}B=0$ and $BA^{\tiny\textcircled{S}}=0$, where $A^{\tiny\textcircled{S}}$ is the generalized core inverse of $A$. The characterizations of C-S orthogonal matries and the C-S additivity are also provided. And the connection between the C-S orthogonality and C-S partial order has been given using their canonical form. Moreover, the concept of the strongly C-S orthogonality is defined and characterized.
Keywords
C-S inverse; C-S orthogonality; Strongly C-S orthogonality; C-S additivity; C-S partial order
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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