2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78577We 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.15 pages, to appear in Michigan Math. JournalAlgebraic GeometryRings and Algebras16R30text