Ranks of a Constrained Hermitian Matrix Expression with Applications

Shao-Wen Yu

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

Abstract: We establish the formulas of the maximal and minimal ranks of the quaternion Hermitian matrix expression C4−A4XA4∗ where X is a Hermitian solution to quaternion matrix equations A1X = C1, XB1 = C2, and A3XA3*=C3. As applications, we give a new necessary and sufficient condition for the existence of Hermitian solution to the system of matrix equations A1X = C1, XB1 = C2, A3XA3*=C3, and A4XA4*=C4, which was investigated by Wang and Wu, 2010, by rank equalities. In addition, extremal ranks of the generalized Hermitian Schur complement C4−A4A3~A4∗ with respect to a Hermitian g‐inverse A3~ of A3, which is a common solution to quaternion matrix equations A1X = C1 and XB1 = C2, are also considered.

Date: 2013
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https://doi.org/10.1155/2013/514984

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:514984

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