Generalized Cayley-Hamilton-Newton identities
نویسنده
چکیده
The q-generalizations of the two fundamental statements of matrix algebra – the Cayley-Hamilton theorem and the Newton relations – to the cases of quantum matrix algebras of an ”RTT-” and of a ”Reflection equation” types have been obtained in [2]–[6]. We construct a family of matrix identities which we call Cayley-HamiltonNewton identities and which underlie the characteristic identity as well as the Newton relations for the RTTand Reflection equation algebras, in the sense that both the characteristic identity and the Newton relations are direct consequences of the CayleyHamilton-Newton identities.
منابع مشابه
0 D ec 1 99 9 Q - multilinear Algebra
The Cayley-Hamilton-Newton theorem which underlies the Newton identities and the Cayley-Hamilton identity is reviewed, first, for the classical matrices with commuting entries, second, for two q-matrix algebras, the RTTalgebra and the RLRL-algebra. The Cayley-Hamilton-Newton identities for these q-algebras are related by the factorization map. A class of algebras M(R̂, F̂ ) is presented. The alge...
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