#### Conference abstracts

Session A2 - Computational Algebraic Geometry - Semi-plenary talk

July 12, 17:00 ~ 17:50 - Room B5

## The Euclidean distance degree of orthogonally invariant matrix varieties.

### Giorgio Ottaviani

### Università di Firenze, Italy - ottavian@math.unifi.it

The closest orthogonal matrix to a real matrix A can be computed by the Singular Value Decomposition of A. Moreover, all the critical points for the Euclidean distance function from A to the variety of orthogonal matrices can be found in a similar way, by restriction to the diagonal case. The number of these critical points is the Euclidean distance degree. We generalize this result to any orthogonally invariant matrix variety. This gives a new perspective on classical results like the Eckart-Young Theorem and also some new results, e.g. on the essential variety in computer vision. At the end of the talk we will touch the case of tensors.

Joint work with Dmitriy Drusvyatskiy (University of Washington, Seattle, USA), Hon-Leung Lee (University of Washington, Seattle, USA) and Rekha R. Thomas (University of Washington, Seattle, USA).