# Orthogonal Invariance and Identifiability

arXiv: https://arxiv.org/abs/1304.1198 · HTML: https://mlsanity.com/paper/1304.1198/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2013.

## Built on by (most cited first, 3 of 3)

- [Active manifolds, stratifications, and convergence to local minima in nonsmooth optimization](https://mlsanity.com/paper/2108.11832/) (2021)
- [The radius of statistical efficiency](https://mlsanity.com/paper/2405.09676/) (2024)
- [Alternating minimization for square root principal component pursuit](https://mlsanity.com/paper/2501.00471/) (2024)

## Abstract (arXiv)

Orthogonally invariant functions of symmetric matrices often inherit properties from their diagonal restrictions: von Neumann's theorem on matrix norms is an early example. We discuss the example of "identifiability", a common property of nonsmooth functions associated with the existence of a smooth manifold of approximate critical points. Identifiability (or its synonym, "partial smoothness") is the key idea underlying active set methods in optimization. Polyhedral functions, in particular, are always partly smooth, and hence so are many standard examples from eigenvalue optimization.