I was searching on google about quotient groups and quotient topology when I read a statement
The quotient group $GL_n(\mathbb{R})$/$P$ (by the right action of $P$) is the same as the Grassmannian set.
I want to know if there is any isomorphism or homomorphism between the set $Gr_k(V)$ and the quotient group $GL_n(\mathbb{R})$/$P$ by the right action of $P$, where $P$ is the subspace $Span$($e_1$,.....,$e_k$) (which is basically an isotropy subgroup of $GL_n(\mathbb{R})$. I am having difficulty knowing why are they both the same? I am familiar with the elements of both spaces but I don't see how are they equal? If there is any simple explanation that could clear up my misunderstanding I would appreciate it.
Thanks