Completing a 2×2 Block Matrix of Real Quaternions with a Partial Specified Inverse
This paper considers a completion problem of a nonsingular 2×2 block matrix over the real quaternion algebra ℍ: Let m1, m2, n1, n2 be nonnegative integers, m1+m2=n1+n2=n>0, and A12∈ℍm1×n2, A21∈ℍm2×n1, A22∈ℍm2×n2, B11∈ℍn1×m1 be given. We determine necessary and sufficient conditions so that the...
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| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/271978 |
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| author | Yong Lin Qing-Wen Wang |
| author_facet | Yong Lin Qing-Wen Wang |
| author_sort | Yong Lin |
| collection | DOAJ |
| description | This paper considers a completion problem of a nonsingular 2×2 block matrix over the real quaternion algebra ℍ: Let m1, m2, n1, n2 be nonnegative integers, m1+m2=n1+n2=n>0, and A12∈ℍm1×n2, A21∈ℍm2×n1, A22∈ℍm2×n2, B11∈ℍn1×m1 be given. We determine necessary and sufficient conditions so that there exists a variant block entry matrix A11∈ℍm1×n1 such that A=(A11A12A21A22)∈ℍn×n is nonsingular, and B11 is the upper left block of a partitioning of A-1. The general expression for A11 is also obtained. Finally, a numerical example is presented to verify the theoretical findings. |
| format | Article |
| id | doaj-art-a2d65790b9f24535b94ef86a49e4b269 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-a2d65790b9f24535b94ef86a49e4b2692025-02-03T05:46:45ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/271978271978Completing a 2×2 Block Matrix of Real Quaternions with a Partial Specified InverseYong Lin0Qing-Wen Wang1Department of Mathematics, Shanghai University, Shanghai 200444, ChinaDepartment of Mathematics, Shanghai University, Shanghai 200444, ChinaThis paper considers a completion problem of a nonsingular 2×2 block matrix over the real quaternion algebra ℍ: Let m1, m2, n1, n2 be nonnegative integers, m1+m2=n1+n2=n>0, and A12∈ℍm1×n2, A21∈ℍm2×n1, A22∈ℍm2×n2, B11∈ℍn1×m1 be given. We determine necessary and sufficient conditions so that there exists a variant block entry matrix A11∈ℍm1×n1 such that A=(A11A12A21A22)∈ℍn×n is nonsingular, and B11 is the upper left block of a partitioning of A-1. The general expression for A11 is also obtained. Finally, a numerical example is presented to verify the theoretical findings.http://dx.doi.org/10.1155/2013/271978 |
| spellingShingle | Yong Lin Qing-Wen Wang Completing a 2×2 Block Matrix of Real Quaternions with a Partial Specified Inverse Journal of Applied Mathematics |
| title | Completing a 2×2 Block Matrix of Real Quaternions with a Partial Specified Inverse |
| title_full | Completing a 2×2 Block Matrix of Real Quaternions with a Partial Specified Inverse |
| title_fullStr | Completing a 2×2 Block Matrix of Real Quaternions with a Partial Specified Inverse |
| title_full_unstemmed | Completing a 2×2 Block Matrix of Real Quaternions with a Partial Specified Inverse |
| title_short | Completing a 2×2 Block Matrix of Real Quaternions with a Partial Specified Inverse |
| title_sort | completing a 2 2 block matrix of real quaternions with a partial specified inverse |
| url | http://dx.doi.org/10.1155/2013/271978 |
| work_keys_str_mv | AT yonglin completinga22blockmatrixofrealquaternionswithapartialspecifiedinverse AT qingwenwang completinga22blockmatrixofrealquaternionswithapartialspecifiedinverse |