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Determinant preserving maps on matrix algebras
Dolinar, Gregor, 11.08.1971- ; Šemrl, Peter
Naj bo ▫$M_n$▫ algebra vseh ▫$n \times n$▫ kompleksnih matrik. Če za surjektivno preslikavo ▫$\phi: M_n \to M_n$▫ velja ▫${\rm det}(A+\lambda B) = {\rm det}(\phi(A)+\lambda\phi(B))$▫, ▫$A,B \in ...M_n$▫, ▫$\lambda \in \Cc$▫, potem je bodisi ▫$\phi(A) = MAN$▫, ▫$A\in M_n$▫ bodisi ▫$\phi$▫ ▫$\phi(A) = MA^tN$▫, ▫$A \in M_n$▫, ▫$M,N \in M_n$▫, kjer sta ▫$M$▫ in ▫$N$▫ taki obrnljivi matriki, da velja ▫${\rm det}(MN)=1$▫.
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