Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2013, Special Issue (2012), Article ID 271978, 5 pages.

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

Yong Lin and Qing-Wen Wang

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Abstract

This paper considers a completion problem of a nonsingular 2 × 2 block matrix over the real quaternion algebra : Let m 1 ,    m 2 ,    n 1 ,    n 2 be nonnegative integers, m 1 + m 2 = n 1 + n 2 = n > 0 , and A 12 m 1 × n 2 ,   A 21 m 2 × n 1 ,   A 22 m 2 × n 2 ,   B 11 n 1 × m 1 be given. We determine necessary and sufficient conditions so that there exists a variant block entry matrix A 11 m 1 × n 1 such that A = ( A 11 A 12 A 21 A 22 ) n × n is nonsingular, and B 11 is the upper left block of a partitioning of A - 1 . The general expression for A 11 is also obtained. Finally, a numerical example is presented to verify the theoretical findings.

Article information

Source
J. Appl. Math., Volume 2013, Special Issue (2012), Article ID 271978, 5 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394807327

Digital Object Identifier
doi:10.1155/2013/271978

Mathematical Reviews number (MathSciNet)
MR3045377

Citation

Lin, Yong; Wang, Qing-Wen. Completing a $2\times2$ Block Matrix of Real Quaternions with a Partial Specified Inverse. J. Appl. Math. 2013, Special Issue (2012), Article ID 271978, 5 pages. doi:10.1155/2013/271978. https://projecteuclid.org/euclid.jam/1394807327


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