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2013 Completing a 2 × 2 Block Matrix of Real Quaternions with a Partial Specified Inverse
Yong Lin, Qing-Wen Wang
J. Appl. Math. 2013(SI03): 1-5 (2013). DOI: 10.1155/2013/271978

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.

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Yong Lin. Qing-Wen Wang. "Completing a 2 × 2 Block Matrix of Real Quaternions with a Partial Specified Inverse." J. Appl. Math. 2013 (SI03) 1 - 5, 2013. https://doi.org/10.1155/2013/271978

Information

Published: 2013
First available in Project Euclid: 14 March 2014

MathSciNet: MR3045377
Digital Object Identifier: 10.1155/2013/271978

Rights: Copyright © 2013 Hindawi

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Vol.2013 • No. SI03 • 2013
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