  In the framework of the Drinfeld theory of twists in Hopf algebras we
construct quantum matrix algebras which generalize the Reflection Equation and
the RTT algebras. Finite-dimensional representations of these algebras related
to the theory of nonultralocal spin chains are presented. The
Cayley-Hamilton-Newton identities are demonstrated. These identities allow to
define the quantum spectrum for the quantum matrices. We mention possible
applications of the new quantum matrix algebras to constructions of
noncommutative analogs of Minkowski space and quantum Poincar\'e algebras.
