四元數(shù)矩陣方程組A-,a-X=C-,a-，XB-,b-=C-,b-，A-,c-XB-,c-=C-,c-的各種對稱解.pdf

1、上海大學(xué)碩士學(xué)位論文四元數(shù)矩陣方程組AX=C，XB=C，AXB=C的各種對稱解姓名：顏淑軍申請學(xué)位級別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：王卿文20100501AbstractInthisdissertation，weinvesigatethe、，a盯ioussymmetric80lutionstothesystemofquaternionmatri)(equatio璐A口X=a，X上站=G，AcX上k=QTheka8tn伽ofthegene

2、ralsolutiontosomesystemsquaternionmatri)【equationsTheser鶴ultsfIlrtherenrichanddevelopethequaternionmatri)【越gebraThedissenationisdiVidedinto3ch印te瑙Inchapter1，we砒roducether鶴earc：hb額岫und，proFess∞andthemainworkwehaVedoneinth

3、isdissertationSomeprelimin甜i髑usedinthispaperareaIs0presentedInchapter2，weco瑚iderthereflexive(orantireae)cive)andP_symmetric(orP8kewsymmetric)solutio璐tothesystemofquatemionmatri](equatio璐AdX=C&，X風(fēng)=G，AcX鼠=GW色givethesolVabi

4、litycoditionsandtheexplicit唧ressionofthesesymmetricsolutionstothesystemsmentionedaboveWb西vema溥malrank。皿LiIlimaLlraIll【andthele嬲tnonntotherefle)(i、resolutioninchapter3，weim—esigatethele鵠t—normofthegeneralcommonsolutiontot

5、hesystemof8i)【quaternionmatri)【equationsA1X=仍，XBl=Q，A2X=傷，X上琵=Q，A3X玩=G，A4X鼠=Gandu鉛thi8conclIlsiontoinvesigatethele弱tnormofthegeneraLlcommonsolutiontosomequaternionmatr恢equationsKeyWbrds：quaternionmatri)【equations，quatern

6、ionmatrb【expr鶴sion，generalizedinverse，symmetric(orskewsymmetric)solution，persymmetric(orpers‰rsymmetnc)solution，rene)cive(orantire丑e)cive)solution，P—symmetric(0rP—skewsymmetric)solution，ma)cimaLlrank，minimalrank，theleast