  We construct a birational equivalence between certain quotients of s-tuples
of equidimensional linear subspaces of $C^n$ and some quotients of products of
square matrices modulo diagonal conjugations. In particular, we prove the
rationality of the quotient space of s-tuples of linear 2-planes in $C^n$
modulo the diagonal $\gl_n(C)$-action . Furthermore, we compute generators of
the field of the rational invariants explicitly.
