convex algebraic geometry
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scholarly journals Bad projections of the PSD cone

2021 ◽  
Author(s):  
Yuhan Jiang ◽  
Bernd Sturmfels
Keyword(s):  
Algebraic Geometry ◽  
Convex Cone ◽  
Positive Semidefinite ◽  
Zariski Closure ◽  
Positive Semidefinite Matrices ◽  
Linear Map ◽  
Convex Algebraic Geometry ◽  
Determinantal Varieties ◽  
Linear Maps

AbstractThe image of the cone of positive semidefinite matrices under a linear map is a convex cone. Pataki characterized the set of linear maps for which that image is not closed. The Zariski closure of this set is a hypersurface in the Grassmannian. Its components are the coisotropic hypersurfaces of symmetric determinantal varieties. We develop the convex algebraic geometry of such bad projections, with focus on explicit computations.

scholarly journals Convex Algebraic Geometry of Curvature Operators

2021 ◽  
Vol 5 (2) ◽  
pp. 200-228
Author(s):  
Renato G. Bettiol ◽  
Mario Kummer ◽  
Ricardo A. E. Mendes
Keyword(s):  
Algebraic Geometry ◽  
Convex Algebraic Geometry

Chapter 1: What is Convex Algebraic Geometry?

2012 ◽  
pp. 1-2
Author(s):  
Grigoriy Blekherman ◽  
Pablo A. Parrilo ◽  
Rekha R. Thomas
Keyword(s):  
Algebraic Geometry ◽  
Convex Algebraic Geometry

Chapter 8: Free Convex Algebraic Geometry

2012 ◽  
pp. 341-405 ◽  
Author(s):  
J. William Helton ◽  
Igor Klep ◽  
Scott McCullough
Keyword(s):  
Algebraic Geometry ◽  
Convex Algebraic Geometry

scholarly journals The Convex algebraic geometry of linear inverse problems

2010 ◽  
Author(s):  
Venkat Chandrasekaran ◽  
Benjamin Recht ◽  
Pablo A. Parrilo ◽  
Alan S. Willsky
Keyword(s):  
Algebraic Geometry ◽  
Inverse Problems ◽  
Linear Inverse Problems ◽  
Convex Algebraic Geometry
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