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<!DOCTYPE ArticleSet PUBLIC "-//NLM//DTD PubMed 2.6//EN" "http://www.ncbi.nlm.nih.gov/corehtml/query/static/PubMed.dtd">
<ArticleSet>
<Article>
<Journal>
				<PublisherName>Iranian Mathematical Society (IMS)</PublisherName>
				<JournalTitle>Bulletin of the Iranian Mathematical Society</JournalTitle>
				<Issn>1017-060X</Issn>
				<Volume>38</Volume>
				<Issue>1</Issue>
				<PubDate PubStatus="epublish">
					<Year>2012</Year>
					<Month>04</Month>
					<Day>01</Day>
				</PubDate>
			</Journal>
<ArticleTitle>Ranks of the common solution to some quaternion matrix equations
with applications</ArticleTitle><FirstPage>131</FirstPage>
			<LastPage>157</LastPage>
			<Language>en</Language>
<AuthorList>
<Author>
					<FirstName>Q. </FirstName>
					<LastName>Wang</LastName>
					<Affiliation>Shanghai University</Affiliation>
				</Author>
<Author>
					<FirstName>S. </FirstName>
					<LastName>Yu</LastName>
					<Affiliation>East China University of Science and Technology</Affiliation>
				</Author>
</AuthorList>
			<History>
				<PubDate PubStatus="received">
					<Year>2010</Year>
					<Month>08</Month>
					<Day>10</Day>
				</PubDate>
			</History>
		<Abstract><![CDATA[We derive the formulas of the maximal andminimal ranks of four real matrices $X_{1},X_{2},X_{3}$ and $X_{4}$in common solution $X=X_{1}+X_{2}i+X_{3}j+X_{4}k$ to quaternionmatrix equations $A_{1}X=C_{1},XB_{2}=C_{2},A_{3}XB_{3}=C_{3}$. Asapplications, we establish necessary and sufficient conditions forthe existence of the common real and complex solutions to the matrixequations. We give the expressions of such solutions to this systemwhen the solvability conditions are met. Moreover, we presentnecessary and sufficient conditions for the existence of real andcomplex solutions to the system of quaternionmatrix equations $A_{1}X=C_{1},XB_{2}=C_{2},A_{3}XB_{3}=C_{3},A_{4}%XB_{4}=C_{4}$. The findings of this paper extend some known resultsin the literature.]]></Abstract>
		<ObjectList>
			<Object Type="keyword">
			<Param Name="value">Quaternion matrix equation</Param>
			</Object>
			<Object Type="keyword">
			<Param Name="value">maximal and minimal rank</Param>
			</Object>
			<Object Type="keyword">
			<Param Name="value">generalized inverse</Param>
			</Object>
			<Object Type="keyword">
			<Param Name="value">real solution</Param>
			</Object>
			<Object Type="keyword">
			<Param Name="value">complex solution</Param>
			</Object>
		</ObjectList>
</Article>
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