We obtain several formulas for the Euclidean distance degree (ED degree) of an arbitrary nonsingular variety in projective space: in terms of Chern and Segre classes, Milnor classes, Chern-Schwartz-MacPherson classes, and an extremely simple formula equating the Euclidean distance degree of X with the Euler characteristic of an open subset of X.

Daniele Andreucci, ∗ Dario Bellaveglia, 2, † Emilio N.M. Cirillo, ‡ and Silvia Marconi § Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza Università di Roma, via A. Scarpa 16, I–00161, Roma, Italy. Dipartimento di Ingegneria Strutturale e Geotecnica Sapienza Università di Roma, via Eudossiana 18, I–00184 Roma, Italy. Dipartimento di Strutture, Università degli Studi Roma T...

We show that the secant variety of the Segre variety gives useful information about the geometrical structure of an arbitrary multipartite quantum system. In particular, we investigate the relation between arbitrary bipartite and three-partite entangled states and this secant variety. We also discuss the geometry of an arbitrary general multipartite state.

In this paper, we propose three real representations of a generalized Segre quaternion matrix. We establish necessary and sufficient conditions for the existence ?-anti-Hermitian solution to system constrained matrix equations over algebra. also obtain expression general when it is solvable. Finally, provide numerical example verify main results paper.