Hi, I am studying some material related to Grassmannians and in particular how to represent k-subspaces of ℝn as "points" in another space. I think understood the general idea behind the Plücker embedding, however, I recently came across another type of embedding (the "Projection embedding") that sounds more intuitive and simpler to understand (see attached figure for its definition). Can anyone elaborate a bit more on the main differences between Plücker and Projection embeddings? In the past I browsed some old textbooks in the classical literature of algebraic geometry, and while the Plücker embedding is always treated extensively, the Projection embedding is not even mentioned at all. Why?