Block Independence in Various Generalized Inverses of Partitioned Quaternion Matrices
Abstract In this paper, we derive some necessary and sufficient conditions for two, three and four quaternion matrices to be block independent in the least squares inverse, the minimum norm inverse and the {1,3,4}-inverse, respectively. Moreover, it is shown that, quite surprisingly, two, three and...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Song, Guangjing [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2018 |
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| Schlagwörter: |
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| Anmerkung: |
© Shiraz University 2018 |
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| Übergeordnetes Werk: |
Enthalten in: Iranian journal of science and technology - Cham, Switzerland : Springer International Pubishing, 2004, 43(2018), 3 vom: 01. März, Seite 1071-1080 |
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| Übergeordnetes Werk: |
volume:43 ; year:2018 ; number:3 ; day:01 ; month:03 ; pages:1071-1080 |
| Links: |
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| DOI / URN: |
10.1007/s40995-018-0534-8 |
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SPR038040735 |
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| 520 | |a Abstract In this paper, we derive some necessary and sufficient conditions for two, three and four quaternion matrices to be block independent in the least squares inverse, the minimum norm inverse and the {1,3,4}-inverse, respectively. Moreover, it is shown that, quite surprisingly, two, three and four ordered quaternion matrices are block independent in the {1,3,4}-inverse if and only if they are block independent in the Moore–Penrose inverse, which at first glance looks to be a weaker condition than the later. | ||
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10.1007/s40995-018-0534-8 doi (DE-627)SPR038040735 (SPR)s40995-018-0534-8-e DE-627 ger DE-627 rakwb eng Song, Guangjing verfasserin aut Block Independence in Various Generalized Inverses of Partitioned Quaternion Matrices 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Shiraz University 2018 Abstract In this paper, we derive some necessary and sufficient conditions for two, three and four quaternion matrices to be block independent in the least squares inverse, the minimum norm inverse and the {1,3,4}-inverse, respectively. Moreover, it is shown that, quite surprisingly, two, three and four ordered quaternion matrices are block independent in the {1,3,4}-inverse if and only if they are block independent in the Moore–Penrose inverse, which at first glance looks to be a weaker condition than the later. System of quaternion matrix equations (dpeaa)DE-He213 Generalized inverse (dpeaa)DE-He213 Block matrix (dpeaa)DE-He213 Zhou, Ying aut Enthalten in Iranian journal of science and technology Cham, Switzerland : Springer International Pubishing, 2004 43(2018), 3 vom: 01. März, Seite 1071-1080 (DE-627)SPR038034816 (DE-600)2843077-3 2364-1819 nnns volume:43 year:2018 number:3 day:01 month:03 pages:1071-1080 https://dx.doi.org/10.1007/s40995-018-0534-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 43 2018 3 01 03 1071-1080 |
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10.1007/s40995-018-0534-8 doi (DE-627)SPR038040735 (SPR)s40995-018-0534-8-e DE-627 ger DE-627 rakwb eng Song, Guangjing verfasserin aut Block Independence in Various Generalized Inverses of Partitioned Quaternion Matrices 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Shiraz University 2018 Abstract In this paper, we derive some necessary and sufficient conditions for two, three and four quaternion matrices to be block independent in the least squares inverse, the minimum norm inverse and the {1,3,4}-inverse, respectively. Moreover, it is shown that, quite surprisingly, two, three and four ordered quaternion matrices are block independent in the {1,3,4}-inverse if and only if they are block independent in the Moore–Penrose inverse, which at first glance looks to be a weaker condition than the later. System of quaternion matrix equations (dpeaa)DE-He213 Generalized inverse (dpeaa)DE-He213 Block matrix (dpeaa)DE-He213 Zhou, Ying aut Enthalten in Iranian journal of science and technology Cham, Switzerland : Springer International Pubishing, 2004 43(2018), 3 vom: 01. März, Seite 1071-1080 (DE-627)SPR038034816 (DE-600)2843077-3 2364-1819 nnns volume:43 year:2018 number:3 day:01 month:03 pages:1071-1080 https://dx.doi.org/10.1007/s40995-018-0534-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 43 2018 3 01 03 1071-1080 |
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10.1007/s40995-018-0534-8 doi (DE-627)SPR038040735 (SPR)s40995-018-0534-8-e DE-627 ger DE-627 rakwb eng Song, Guangjing verfasserin aut Block Independence in Various Generalized Inverses of Partitioned Quaternion Matrices 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Shiraz University 2018 Abstract In this paper, we derive some necessary and sufficient conditions for two, three and four quaternion matrices to be block independent in the least squares inverse, the minimum norm inverse and the {1,3,4}-inverse, respectively. Moreover, it is shown that, quite surprisingly, two, three and four ordered quaternion matrices are block independent in the {1,3,4}-inverse if and only if they are block independent in the Moore–Penrose inverse, which at first glance looks to be a weaker condition than the later. System of quaternion matrix equations (dpeaa)DE-He213 Generalized inverse (dpeaa)DE-He213 Block matrix (dpeaa)DE-He213 Zhou, Ying aut Enthalten in Iranian journal of science and technology Cham, Switzerland : Springer International Pubishing, 2004 43(2018), 3 vom: 01. März, Seite 1071-1080 (DE-627)SPR038034816 (DE-600)2843077-3 2364-1819 nnns volume:43 year:2018 number:3 day:01 month:03 pages:1071-1080 https://dx.doi.org/10.1007/s40995-018-0534-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 43 2018 3 01 03 1071-1080 |
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10.1007/s40995-018-0534-8 doi (DE-627)SPR038040735 (SPR)s40995-018-0534-8-e DE-627 ger DE-627 rakwb eng Song, Guangjing verfasserin aut Block Independence in Various Generalized Inverses of Partitioned Quaternion Matrices 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Shiraz University 2018 Abstract In this paper, we derive some necessary and sufficient conditions for two, three and four quaternion matrices to be block independent in the least squares inverse, the minimum norm inverse and the {1,3,4}-inverse, respectively. Moreover, it is shown that, quite surprisingly, two, three and four ordered quaternion matrices are block independent in the {1,3,4}-inverse if and only if they are block independent in the Moore–Penrose inverse, which at first glance looks to be a weaker condition than the later. System of quaternion matrix equations (dpeaa)DE-He213 Generalized inverse (dpeaa)DE-He213 Block matrix (dpeaa)DE-He213 Zhou, Ying aut Enthalten in Iranian journal of science and technology Cham, Switzerland : Springer International Pubishing, 2004 43(2018), 3 vom: 01. März, Seite 1071-1080 (DE-627)SPR038034816 (DE-600)2843077-3 2364-1819 nnns volume:43 year:2018 number:3 day:01 month:03 pages:1071-1080 https://dx.doi.org/10.1007/s40995-018-0534-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 43 2018 3 01 03 1071-1080 |
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10.1007/s40995-018-0534-8 doi (DE-627)SPR038040735 (SPR)s40995-018-0534-8-e DE-627 ger DE-627 rakwb eng Song, Guangjing verfasserin aut Block Independence in Various Generalized Inverses of Partitioned Quaternion Matrices 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Shiraz University 2018 Abstract In this paper, we derive some necessary and sufficient conditions for two, three and four quaternion matrices to be block independent in the least squares inverse, the minimum norm inverse and the {1,3,4}-inverse, respectively. Moreover, it is shown that, quite surprisingly, two, three and four ordered quaternion matrices are block independent in the {1,3,4}-inverse if and only if they are block independent in the Moore–Penrose inverse, which at first glance looks to be a weaker condition than the later. System of quaternion matrix equations (dpeaa)DE-He213 Generalized inverse (dpeaa)DE-He213 Block matrix (dpeaa)DE-He213 Zhou, Ying aut Enthalten in Iranian journal of science and technology Cham, Switzerland : Springer International Pubishing, 2004 43(2018), 3 vom: 01. März, Seite 1071-1080 (DE-627)SPR038034816 (DE-600)2843077-3 2364-1819 nnns volume:43 year:2018 number:3 day:01 month:03 pages:1071-1080 https://dx.doi.org/10.1007/s40995-018-0534-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 43 2018 3 01 03 1071-1080 |
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Block Independence in Various Generalized Inverses of Partitioned Quaternion Matrices |
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Abstract In this paper, we derive some necessary and sufficient conditions for two, three and four quaternion matrices to be block independent in the least squares inverse, the minimum norm inverse and the {1,3,4}-inverse, respectively. Moreover, it is shown that, quite surprisingly, two, three and four ordered quaternion matrices are block independent in the {1,3,4}-inverse if and only if they are block independent in the Moore–Penrose inverse, which at first glance looks to be a weaker condition than the later. © Shiraz University 2018 |
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Abstract In this paper, we derive some necessary and sufficient conditions for two, three and four quaternion matrices to be block independent in the least squares inverse, the minimum norm inverse and the {1,3,4}-inverse, respectively. Moreover, it is shown that, quite surprisingly, two, three and four ordered quaternion matrices are block independent in the {1,3,4}-inverse if and only if they are block independent in the Moore–Penrose inverse, which at first glance looks to be a weaker condition than the later. © Shiraz University 2018 |
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Abstract In this paper, we derive some necessary and sufficient conditions for two, three and four quaternion matrices to be block independent in the least squares inverse, the minimum norm inverse and the {1,3,4}-inverse, respectively. Moreover, it is shown that, quite surprisingly, two, three and four ordered quaternion matrices are block independent in the {1,3,4}-inverse if and only if they are block independent in the Moore–Penrose inverse, which at first glance looks to be a weaker condition than the later. © Shiraz University 2018 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR038040735</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230328194923.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201007s2018 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s40995-018-0534-8</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR038040735</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s40995-018-0534-8-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Song, Guangjing</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Block Independence in Various Generalized Inverses of Partitioned Quaternion Matrices</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2018</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Shiraz University 2018</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In this paper, we derive some necessary and sufficient conditions for two, three and four quaternion matrices to be block independent in the least squares inverse, the minimum norm inverse and the {1,3,4}-inverse, respectively. Moreover, it is shown that, quite surprisingly, two, three and four ordered quaternion matrices are block independent in the {1,3,4}-inverse if and only if they are block independent in the Moore–Penrose inverse, which at first glance looks to be a weaker condition than the later.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">System of quaternion matrix equations</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Generalized inverse</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Block matrix</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Zhou, Ying</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Iranian journal of science and technology</subfield><subfield code="d">Cham, Switzerland : Springer International Pubishing, 2004</subfield><subfield code="g">43(2018), 3 vom: 01. März, Seite 1071-1080</subfield><subfield code="w">(DE-627)SPR038034816</subfield><subfield code="w">(DE-600)2843077-3</subfield><subfield code="x">2364-1819</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:43</subfield><subfield code="g">year:2018</subfield><subfield code="g">number:3</subfield><subfield code="g">day:01</subfield><subfield code="g">month:03</subfield><subfield code="g">pages:1071-1080</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/s40995-018-0534-8</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">43</subfield><subfield code="j">2018</subfield><subfield code="e">3</subfield><subfield code="b">01</subfield><subfield code="c">03</subfield><subfield code="h">1071-1080</subfield></datafield></record></collection>
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7.401434 |