
Grassmannians
Grassmannians are mathematical spaces that represent all possible ways to select a fixed-size linear subspace within a larger vector space. For example, imagine all possible planes within a three-dimensional space; the set of these planes forms a Grassmannian. They provide a way to study the geometry of these subspaces collectively, capturing their relationships and positions. Grassmannians are fundamental in fields like geometry, algebra, and data analysis because they help describe how subspaces of vectors can vary systematically within a larger space.