v2007.09.17 - Convex Optimization

686 APPENDIX G. NOTATION AND A FEW DEFINITIONScard cardinality, cardx ∆ = ‖x‖ 0convcenvconeconvex hullconvex envelopeconic hullcontent content of high-dimensional bounded polyhedron, volume in 3dimensions, area in 2, and so oncofdistmatrix of cofactors corresponding to matrix argumentdistance between point or set argumentsvec vectorization of m ×n matrix, Euclidean dimension mn (30)svec vectorization of symmetric n ×n matrix, Euclidean dimensionn(n + 1)/2 (47)dvecvectorization of symmetric hollow n ×n matrix, Euclidean dimensionn(n − 1)/2 (63)(x,y) angle between vectors x and y , or dihedral angle between affinesubsets≽≻⊁≥generalized inequality; e.g., A ≽ 0 means vector or matrix A must beexpressible in a biorthogonal expansion having nonnegative coordinateswith respect to extreme directions of some implicit pointed closed convexcone K , or comparison to the origin with respect to some implicitpointed closed convex cone, or (when K= S+) n matrix A belongs to thepositive semidefinite cone of symmetric matrices (2.9.0.1), or (whenK= R n +) vector A belongs to the nonnegative orthant (each vector entryis nonnegative,2.3.1.1)strict generalized inequalitynot positive definitescalar inequality, greater than or equal to; comparison of scalars,or entrywise comparison of vectors or matrices with respect to R +nonnegative for α∈ R , α ≥ 0