Completing a 2 × 2 Block Matrix of Real Quaternions with a Partial Specified Inverse

Yong Lin and Qing-Wen Wang

Journal of Applied Mathematics, 2013, vol. 2013, issue 1

Abstract: 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.

Date: 2013
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2013/271978

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:271978

Access Statistics for this article

More articles in Journal of Applied Mathematics from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().