# The Two Lives of the Grassmannian

arXiv: https://arxiv.org/abs/2401.03684 · HTML: https://mlsanity.com/paper/2401.03684/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jan 2024.

## Built on by (most cited first, 1 of 1)

- [Pointwise Generalization in Deep Neural Networks](https://mlsanity.com/paper/2605.18598/) (2026)

## Abstract (arXiv)

The real Grassmannian is both a projective variety (via Pl"ucker coordinates) and an affine variety (via orthogonal projections). We connect these two representations, and we develop the commutative algebra of the latter variety. We introduce the squared Grassmannian, and we study applications to determinantal point processes in statistics.