A NOTE OF MULTIPLICATIVE MAPS ON MATRICES THAT PRESERVE THE SPECTRUM

(整期优先)网络出版时间:2000-06-27
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LetUn(C),GLn(C)andMn(C)bethen-degreeunitarygroup,thenn-degreegenerallineargroupandthesemigroupsofalln×nmatricesovercomplexnumberfieldCrespec-tively.Hochwaldin[1]showedthatiff:Un(C)→Mn(C)isaspectrum-preservingmulti-plicativemap,thenthereexistsamatrixRinGLn(C)suchthatf(A)=R-1ARforallA∈