We provide a closed formula for the degree of SO (n, ℂ). In addition, we test symbolic and numerical techniques for computing the degree of SO (n, ℂ). As an application of our results, we give a formula for the number of critical points of a low-rank semidefinite programming problem. Finally, we provide evidence for a conjecture regarding the real locus of SO (n, ℂ).
CITATION STYLE
Brandt, M., Bruce, J., Brysiewicz, T., Krone, R., & Robeva, E. (2017). The degree of SO(n, ℂ). In Fields Institute Communications (Vol. 80, pp. 229–246). Springer New York LLC. https://doi.org/10.1007/978-1-4939-7486-3_11
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