  We revise a monogenic calculus for several non-commuting operators, which is
defined through group representations. Instead of an algebraic homomorphism we
use group covariance. The related notion of joint spectrum and spectral mapping
theorem are discussed. The construction is illustrated by a simple example of
calculus and joint spectrum of two non-commuting selfadjoint (n\times n)
matrices.
  Keywords: Functional calculus, spectrum, intertwining operator, spectral
mapping theorem, jet spaces, monogenic function, Clifford algebra
