Grassmannian

The Grassmannian is a mathematical concept that describes all possible subspaces of a particular dimension within a larger space. Imagine a vast collection of flat surfaces or lines within a higher-dimensional space; the Grassmannian organizes these subspaces in a systematic way. For example, it encompasses all possible planes in three-dimensional space or all lines in four-dimensional space. It’s a fundamental tool in geometry and algebra for studying how these subspaces relate, transform, and connect within larger spaces, providing a structured way to analyze complex geometric and algebraic relationships.