The degree of $\text{SO}(n)$

Madeline Brandt; DJ Bruce; Taylor Brysiewicz; Robert Krone; Elina Robeva

The degree of $\text{SO}(n)$

Algebraic Geometry 2017-01-16 v2

Authors: Madeline Brandt , DJ Bruce , Taylor Brysiewicz , Robert Krone , Elina Robeva

Abstract

We provide a closed formula for the degree of $\text{SO}(n)$ over an algebraically closed field of characteristic zero. In addition, we describe symbolic and numerical techniques which can also be used to compute the degree of $\text{SO}(n)$ for small values of $n$ . As an application of our results, we give a formula for the number of critical points of a low-rank semidefinite programming optimization problem. Finally, we provide some evidence for a conjecture regarding the real locus of $\text{SO}(n)$ .

Keywords

degree of SO(n) algebraically closed field semidefinite programming critical points real locus symbolic computation numerical techniques

Cite

@article{arxiv.1701.03200,
  title  = {The degree of $\text{SO}(n)$},
  author = {Madeline Brandt and DJ Bruce and Taylor Brysiewicz and Robert Krone and Elina Robeva},
  journal= {arXiv preprint arXiv:1701.03200},
  year   = {2017}
}

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21 pages, 3 figures

The degree of $\text{SO}(n)$

Abstract

Keywords

Cite

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