The Euclidean distance degree of a real variety is an important invariant arising in distance minimization problems. We show that the Eu- clidean 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.
THE EUCLIDEAN DISTANCE DEGREE OF ORTHOGONALLY INVARIANT MATRIX VARIETIES / Dmitriy, Drusvyatskiy; HON LEUNG LEE, ; Ottaviani, GIORGIO MARIA; Thomas, REKHA R.. - In: ISRAEL JOURNAL OF MATHEMATICS. - ISSN 0021-2172. - STAMPA. - 221:(2017), pp. 291-316. [10.1007/s11856-017-1545-4]
THE EUCLIDEAN DISTANCE DEGREE OF ORTHOGONALLY INVARIANT MATRIX VARIETIES
OTTAVIANI, GIORGIO MARIA;
2017
Abstract
The Euclidean distance degree of a real variety is an important invariant arising in distance minimization problems. We show that the Eu- clidean 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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