Ranks of a Constrained Hermitian Matrix Expression with Applications

Shao-Wen Yu

Journal of Applied Mathematics, 2013, vol. 2013, 1-9

Abstract:

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

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:514984

DOI: 10.1155/2013/514984

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