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The euclidean distance degree of orthogonally invariant matrix varieties |
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| Authors: | Dmitriy Drusvyatskiy Hon-Leung Lee Giorgio Ottaviani Rekha R Thomas |
| Institution: | 1.Department of Mathematics,University of Washington,Seattle,USA;2.DIMAI,Università di Firenze,Firenze,Italy;3.Department of Mathematics,University of Washington,Seattle,USA |
| Abstract: | The Euclidean distance degree of a real variety is an important invariant arising in distance minimization problems. We show that the Euclidean distance degree of an orthogonally invariant matrix variety equals the Euclidean distance degree of its restriction to diagonal matrices. We illustrate how this result can greatly simplify calculations in concrete circumstances. |
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