The characteristic polynomial in calculation of exponential and
elementary functions in Clifford algebras
Formulas to calculate multivector exponentials in a basis-free
representation and orthonormal basis are presented for an arbitrary
Clifford geometric algebra , . The formulas are based on
the analysis of roots of characteristic polynomial of a multivector.
Elaborate examples how to use the formulas in practice are presented.
The results are generalised to arbitrary functions of multivector and
may be useful in the quantum circuits or in the problems of analysis of
evolution of the entangled quantum states.