Further results on strongly core orthogonal matrix

Liu, Xiaoji; Wang, Congcong; Wang, Hongxing

doi:10.1080/03081087.2022.2111544

Cited by 3 publications

(2 citation statements)

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“…In [3], we can see that A ⊥ s, # ⃝ B implies (A + B) # ⃝ = A # ⃝ + B # ⃝ (core additivity). In [4], Liu, Wang, and Wang proved that A, B ∈ C n×n with Ind(A) ≤ 1 and Ind(B) ≤ 1 are strongly core orthogonal, if and only if (A + B) # ⃝ = A # ⃝ + B # ⃝ and A # ⃝ B = 0 (or BA # ⃝ = 0), instead of A ⊥ # ⃝ B, which is more concise than Theorem 7.3 in [3]. And, Ferreyra and Malik in [3], have proven that if A is strongly core orthogonal to B, then rk(A + B) =rk(A)+rk(B) and (A + B) # ⃝ = A # ⃝ + B # ⃝ .…”

Section: Introductionmentioning

confidence: 99%

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C-S and Strongly C-S Orthogonal Matrices

Liu,

Jin

2024

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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 ASB=0 and BAS=0, where AS is the generalized core inverse of A. The characterizations of C-S orthogonal matrices 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.

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Section: Introductionmentioning

confidence: 99%

“…But, whether the reverse holds is still an open question. In [4], Liu, Wang, and Wang solved the problem completely. Furthermore, they also gave some new equivalent conditions for the strongly core orthogonality, which are related to the minus partial order and some Hermitian matrices.…”

Section: Introductionmentioning

confidence: 99%

C-S and Strongly C-S Orthogonal Matrices

Liu,

Jin

2024

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Core partial order and core orthogonality comparing with star partial order and star orthogonality

Zou,

Mosić,

Zhu

et al. 2024

Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat.

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C-S and Strongly C-S Orthogonal Matrices

Liu,

Jin

2023

Preprint

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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.

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Further results on strongly core orthogonal matrix

Cited by 3 publications

References 31 publications

C-S and Strongly C-S Orthogonal Matrices

C-S and Strongly C-S Orthogonal Matrices

Core partial order and core orthogonality comparing with star partial order and star orthogonality

C-S and Strongly C-S Orthogonal Matrices

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