On the degree of varieties of sum of squares
Permanent link
https://hdl.handle.net/10037/34924Date
2024-02-10Type
Journal articleTidsskriftartikkel
Peer reviewed
Abstract
We study the problem of how many different sum of squares decompositions a general polynomial f with SOS-rank k admits. We show that there is a link between the variety SOSk(f) of all SOS-decompositions of f and the orthogonal group O(k). We exploit this connection to obtain the dimension of SOSk(f) and show that its degree is bounded from below by the degree of O (k). In particular, for k = 2 we show that SOS2(f) is isomorphic to O(2)
and hence the degree bound becomes an equality. Moreover, we compute the dimension of the space of polynomials of SOS-rank k and obtain the degree in the special case k = 2.
Publisher
ElsevierCitation
Ferguson, Ottaviani, Safey el Din, Teixeira Turatti. On the degree of varieties of sum of squares. Journal of Pure and Applied Algebra. 2024;228(7)Metadata
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Copyright 2024 The Author(s)