We elaborate on a problem raised by Schmidt in 1967 which generalizes
the theory of classical Diophantine approximation to subspaces of
.
We consider Diophantine exponents for linear subspaces of
which
generalize the irrationality measure for real numbers. We prove here that we have no
smooth relations among some functions associated to these exponents. To establish
this result, we construct subspaces for which we are able to compute the
exponents.