  We consider the relations of generalized commutativity in the algebra of
formal series $ M_q (x^i ) $, which conserve a tensor $ I_q $-grading and
depend on parameters $ q(i,k) $ . We choose the $ I_q $-preserving version of
differential calculus on $ M_q$ . A new construction of the symmetrized tensor
product for $ M_q $-type algebras and the corresponding definition of minimally
deformed linear group $ QGL(n) $ and Lie algebra $ qgl(n) $ are proposed. We
study the connection of $ QGL(n) $ and $ qgl(n) $ with the special matrix
algebra $ \mbox{Mat} (n,Q) $ containing matrices with noncommutative elements.
A definition of the deformed determinant in the algebra $ \mbox{Mat} (n,Q) $ is
given. The exponential parametrization in the algebra $ \mbox{Mat} (n,Q) $ is
considered on the basis of Campbell-Hausdorf formula.
