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2013 Ranks of a Constrained Hermitian Matrix Expression with Applications
Shao-Wen Yu
J. Appl. Math. 2013(SI03): 1-9 (2013). DOI: 10.1155/2013/514984

Abstract

We establish the formulas of the maximal and minimal ranks of the quaternion Hermitian matrix expression C 4 A 4 X A 4 where X is a Hermitian solution to quaternion matrix equations A 1 X = C 1 , X B 1 = C 2 , and A 3 X A 3 * = C 3 . As applications, we give a new necessary and sufficient condition for the existence of Hermitian solution to the system of matrix equations A 1 X = C 1 , X B 1 = C 2 , A 3 X A 3 * = C 3 , and A 4 X A 4 * = C 4 , which was investigated by Wang and Wu, 2010, by rank equalities. In addition, extremal ranks of the generalized Hermitian Schur complement C 4 A 4 A 3 ~ A 4 with respect to a Hermitian g-inverse A 3 ~ of A 3 , which is a common solution to quaternion matrix equations A 1 X = C 1 and X B 1 = C 2 , are also considered.

Erratum to “Ranks of a Constrained Hermitian Matrix Expression with Applications” dx.doi.org/10.1155/2013/826397

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Shao-Wen Yu. "Ranks of a Constrained Hermitian Matrix Expression with Applications." J. Appl. Math. 2013 (SI03) 1 - 9, 2013. https://doi.org/10.1155/2013/514984

Information

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

zbMATH: 1266.15028
MathSciNet: MR3032253
Digital Object Identifier: 10.1155/2013/514984

Rights: Copyright © 2013 Hindawi

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Vol.2013 • No. SI03 • 2013
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