C-S and Strongly C-S Orthogonal Matrices
In this paper, we present a new concept of the generalized core orthogonality (called the C-S orthogonality) for two generalized core invertible matrices <i>A</i> and <i>B</i>. <i>A</i> is said to be C-S orthogonal to <i>B</i> if <inline-formula>...
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MDPI AG
2024-02-01
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| Online Access: | https://www.mdpi.com/2075-1680/13/2/110 |
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| author | Xiaoji Liu Ying Liu Hongwei Jin |
| author_facet | Xiaoji Liu Ying Liu Hongwei Jin |
| author_sort | Xiaoji Liu |
| collection | DOAJ |
| description | In this paper, we present a new concept of the generalized core orthogonality (called the C-S orthogonality) for two generalized core invertible matrices <i>A</i> and <i>B</i>. <i>A</i> is said to be C-S orthogonal to <i>B</i> if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>A</mi><mrow><menclose notation="circle"><mi mathvariant="normal">S</mi></menclose></mrow></msup><mi>B</mi><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>B</mi><msup><mi>A</mi><mrow><menclose notation="circle"><mi mathvariant="normal">S</mi></menclose></mrow></msup><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>A</mi><mrow><menclose notation="circle"><mi mathvariant="normal">S</mi></menclose></mrow></msup></semantics></math></inline-formula> is the generalized core inverse of <i>A</i>. 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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| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-07T22:42:56Z |
| publishDate | 2024-02-01 |
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| spelling | doaj.art-bd3f98c3fa2a426598f06f8b3d6b45932024-02-23T15:07:26ZengMDPI AGAxioms2075-16802024-02-0113211010.3390/axioms13020110C-S and Strongly C-S Orthogonal MatricesXiaoji Liu0Ying Liu1Hongwei Jin2School of Education, Guangxi Vocational Normal University, Nanning 530007, ChinaSchool of Mathematics and Physics, Guangxi Minzu University, Nanning 530006, ChinaSchool of Mathematics and Physics, Guangxi Minzu University, Nanning 530006, ChinaIn this paper, we present a new concept of the generalized core orthogonality (called the C-S orthogonality) for two generalized core invertible matrices <i>A</i> and <i>B</i>. <i>A</i> is said to be C-S orthogonal to <i>B</i> if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>A</mi><mrow><menclose notation="circle"><mi mathvariant="normal">S</mi></menclose></mrow></msup><mi>B</mi><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>B</mi><msup><mi>A</mi><mrow><menclose notation="circle"><mi mathvariant="normal">S</mi></menclose></mrow></msup><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>A</mi><mrow><menclose notation="circle"><mi mathvariant="normal">S</mi></menclose></mrow></msup></semantics></math></inline-formula> is the generalized core inverse of <i>A</i>. 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.https://www.mdpi.com/2075-1680/13/2/110C-S inverseC-S orthogonalitystrongly C-S orthogonalityC-S additivityC-S partial order |
| spellingShingle | Xiaoji Liu Ying Liu Hongwei Jin C-S and Strongly C-S Orthogonal Matrices Axioms C-S inverse C-S orthogonality strongly C-S orthogonality C-S additivity C-S partial order |
| title | C-S and Strongly C-S Orthogonal Matrices |
| title_full | C-S and Strongly C-S Orthogonal Matrices |
| title_fullStr | C-S and Strongly C-S Orthogonal Matrices |
| title_full_unstemmed | C-S and Strongly C-S Orthogonal Matrices |
| title_short | C-S and Strongly C-S Orthogonal Matrices |
| title_sort | c s and strongly c s orthogonal matrices |
| topic | C-S inverse C-S orthogonality strongly C-S orthogonality C-S additivity C-S partial order |
| url | https://www.mdpi.com/2075-1680/13/2/110 |
| work_keys_str_mv | AT xiaojiliu csandstronglycsorthogonalmatrices AT yingliu csandstronglycsorthogonalmatrices AT hongweijin csandstronglycsorthogonalmatrices |