0 D ec 1 99 9 Q - multilinear Algebra
نویسنده
چکیده
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 algebras M(R̂, F̂ ) include the RTT-algebra and the RLRL-algebra as particular cases. The algebra M(R̂, F̂ ) is defined by a pair of compatible matrices R̂ and F̂ . The Cayley-Hamilton-Newton theorem for the algebras M(R̂, F̂ ) is stated. A nontrivial example of a compatible pair is given. On leave of absence from P. N. Lebedev Physical Institute, Leninsky Pr. 53, 117924 Moscow, Russia
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