简介：Inthispaper,theGH-congruencecanonicalformsofpositivesemidefiniteanddefinteiniteanddefinite(neednotbeself-conjugate)quaternionmatricesaregiven,andaneccessaryandsufficientconditionofGH-congruencefortwopositivesemidifinite(definite)quaternionmatricesisgivenalso.ThensimultaneousGH-congruencereducedformsfortwoself-conjugatematri-cesandsomeresultaboutthesimultaneousGH-congruencediagonalizationofquaternionmatricesareobtained.
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