Completing a 2×2 Block Matrix of Real Quaternions with a Partial Specified Inverse
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-5, 5 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-04-10
Country of Publication
Egypt
No. of Pages
5
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Lin, Yong& Wang, Qing-Wen. 2013. Completing a 2×2 Block Matrix of Real Quaternions with a Partial Specified Inverse. Journal of Applied Mathematics،Vol. 2013, no. 2013, pp.1-5.
https://search.emarefa.net/detail/BIM-459250
Modern Language Association (MLA)
Lin, Yong& Wang, Qing-Wen. Completing a 2×2 Block Matrix of Real Quaternions with a Partial Specified Inverse. Journal of Applied Mathematics No. 2013 (2013), pp.1-5.
https://search.emarefa.net/detail/BIM-459250
American Medical Association (AMA)
Lin, Yong& Wang, Qing-Wen. Completing a 2×2 Block Matrix of Real Quaternions with a Partial Specified Inverse. Journal of Applied Mathematics. 2013. Vol. 2013, no. 2013, pp.1-5.
https://search.emarefa.net/detail/BIM-459250
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-459250