Geodesic
Extreme ranks of (skew-)Hermitian solutions to a quaternion matrix equation
The electronic journal of linear algebra, Tome 20 (2010), pp. 552-573.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The extreme ranks, i.e., the maximal and minimal ranks, are established for the general Hermitian solution as well as the general skew-Hermitian solution to the classical matrix equation AXA * + BY B * = C over the quaternion algebra. Also given in this paper are the formulas of extreme ranks of real matrices X i , Y i , i = 1, $\cdot \cdot \cdot , 4,$ in a pair (skew-)Hermitian solution X = X
Classification : 15A03, 15A09, 15A24, 15A33
Keywords: quaternion matrix equation, minimal rank, maximal rank, Hermitian solution, skew-Hermitian solution 
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     author = {Wang, Qing-Wen and Jing, Jiang},
     title = {Extreme ranks of {(skew-)Hermitian} solutions to a quaternion matrix equation},
     journal = {The electronic journal of linear algebra},
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     publisher = {mathdoc},
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     year = {2010},
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     url = {http://geodesic.mathdoc.fr/item/ELA_2010__20__a14/}
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Wang, Qing-Wen; Jing, Jiang. Extreme ranks of (skew-)Hermitian solutions to a quaternion matrix equation. The electronic journal of linear algebra, Tome 20 (2010), pp. 552-573. http://geodesic.mathdoc.fr/item/ELA_2010__20__a14/