<?xml version="1.0" encoding="UTF-8"?>
<!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>37</Volume>
				<Issue>No. 3</Issue>
				<PubDate PubStatus="epublish">
					<Year>2011</Year>
					<Month>09</Month>
					<Day>15</Day>
				</PubDate>
			</Journal>
<ArticleTitle>The (R,S)-symmetric and (R,S)-skew symmetric solutions of the pair of matrix equations A1XB1 = C1 and A2XB2 = C2</ArticleTitle><FirstPage>269</FirstPage>
			<LastPage>279</LastPage>
			<Language>en</Language>
<AuthorList>
<Author>
					<FirstName>M. </FirstName>
					<LastName>Dehghan</LastName>
					<Affiliation></Affiliation>
				</Author>
<Author>
					<FirstName>M. </FirstName>
					<LastName>Hajarian</LastName>
					<Affiliation></Affiliation>
				</Author>
</AuthorList>
			<History>
				<PubDate PubStatus="received">
					<Year>2009</Year>
					<Month>02</Month>
					<Day>03</Day>
				</PubDate>
			</History>
		<Abstract><![CDATA[Let $Rin textbf{C}^{mtimes m}$ and $Sin textbf{C}^{ntimes n}$ be nontrivial involution matrices; i.e.,  $R=R^{-1}neq pm~I$ and $S=S^{-1}neq pm~I$.
 An $mtimes n$ complex matrix $A$ is said to be an $(R, S)$-symmetric ($(R, S)$-skew symmetric) matrix if $RAS =A$ ($ RAS =-A$).
The $(R, S)$-symmetric and $(R, S)$-skew symmetric matrices have
a number of special properties and widely used in engineering and
scientific computating. Here, we introduce the necessary and
sufficient conditions for the solvability of the pair of matrix
equations $A_{1}XB_{1}=C_{1}$ and $A_{2}XB_{2}=C_{2}$, over  $(R,
S)$-symmetric and $(R, S)$-skew symmetric  matrices, and give the
general expressions of the solutions for the solvable cases.
Finally, we give necessary and sufficient conditions for the
existence of $(R, S)$-symmetric and $(R, S)$-skew symmetric
solutions and representations of these solutions to the pair of
matrix equations in some special cases.]]></Abstract>
		<ObjectList>
			<Object Type="keyword">
			<Param Name="value">Matrix equation</Param>
			</Object>
			<Object Type="keyword">
			<Param Name="value">(R</Param>
			</Object>
			<Object Type="keyword">
			<Param Name="value">S)-symmetric matrix</Param>
			</Object>
			<Object Type="keyword">
			<Param Name="value">S)-skew symmetric matrix</Param>
			</Object>
		</ObjectList>
</Article>
</ArticleSet>