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∈