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1、:41:3=f))Vol.41,No.3199885NACTAMATHEMATICASINICAMay,1998/18
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2、tionsbetweenSomeConceptionsintheQuaternionMatrixTheoryLiYangming(DepartmentofMathematics,GuangdongCollegeofEducation,Guangzhou510303,China)AbstractInthispaper,wepointoutandcorrecttheerrorinpaper[1],givetherelationbetweentheweaklycharacteristicpolynomial[2]andthedoublecharacteris-ticpoly
3、nomial[3],aswellastherelationbetweenthedeterminant[2]andthedoubledeterminant[4],atlastwediscusstherelationamongtherighteigenvalue,lefteigen-value,eigenvalueandcharacteristicroot,aswellastherelationbetweentherootsoftheminimalpolynomialandtherootsoftheweeklycharacteristicpolynomial.Keywor
4、dsError,Minimalpolynomal,Weaklycharacteristicpolynomial,Characteris-ticsroot,Eigenvalue,Complexrepresentationmatrix1991MRSubjectClassification15A15ChineseLibraryClassificationO151.21$[1]7;%,H_
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8、=R(YdH),HF=HRYiJdvFi−2ki0A=i,B=,00iRRFAfJmW!5tvRA=HR.CF1jn×nP=∈R,01AP6VR−11−ji−2k1ji0PAP===B,0101010i2rA,BPRAfl1HA=RBHB=C(IdH),AA5w@[λ+1,BB5w@[λ−i,F“3”F“3u”a4S^Yp[1]“5”515
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10、λ)n×n1sHA∩FA[λ]Sdm5[(da1@[R*P6VP∈F,Z4P−1AP=diag{A,A,···,A},12sAAi5w@[qi(λ)5[”>'“5”r%[1]f“6”r[1]“6”M_[H5@DX9iJdvFYiJdvYdS_1-5U%cE4r,cPYiJdvfVRYdHC]IdHHR=R+Ri+Rj+Rk,ij=−ji=kYiJdv)∈Hn×n,+VA=(aijRRA=(aij),BdetA]WP[5]f95#[
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