%0 Journal Article %T Euclidean Distance degrees of real algebraic groups %A Jasmijn A. Baaijens %A Jan Draisma %J Mathematics %D 2014 %I arXiv %X We study the problem of finding, in a real algebraic matrix group, the matrix closest to a given data matrix. We do so from the algebro-geometric perspective of Euclidean distance degrees. We recover several classical results; and among the new results that we prove is a formula for the Euclidean distance degree of special linear groups. %U http://arxiv.org/abs/1405.0422v1