  Diagonalization of uncertainty matrix and minimization of Robertson
inequality for n observables are considered. It is proved that for even n this
relation is minimized in states which are eigenstates of n/2 independent
complex linear combinations of the observables. In case of canonical
observables this eigenvalue condition is also necessary. Such minimizing states
are called Robertson intelligent states (RIS).
  The group related coherent states (CS) with maximal symmetry (for semisimple
Lie groups) are particular case of RIS for the quadratures of Weyl generators.
Explicit constructions of RIS are considered for operators of su(1,1), su(2),
h_N and sp(N,R) algebras. Unlike the group related CS, RIS can exhibit strong
squeezing of group generators. Multimode squared amplitude squeezed states are
naturally introduced as sp(N,R) RIS. It is shown that the uncertainty matrices
for quadratures of q-deformed boson operators a_{q,j} (q > 0) and of any k
power of a_j = a_{1,j} are positive definite and can be diagonalized by
symplectic linear transformations. PACS numbers: 03.65.Fd, 42.50.Dv
