v2010.10.26 - Convex Optimization

777X point list ((76) having cardinality N) arranged columnar in R n×N ,or set of generators, or extreme directions, or matrix variableGrkknNinonontooverone-to-oneepidomRfGram matrix X T Xaffine dimensionnumber of conically independent generatorsraw-data domain of Magnetic Resonance Imaging machine as in k-spaceEuclidean (ambient spatial) dimension of list X ∈ R n×N , or integercardinality of list X ∈ R n×N , or integerfunction f in x means x as argument to for x in C means element x is a member of set Cfunction f(x) on A means A is domfor relation ≼ on A means A is set whose elements are subject to ≼or projection of x on A means A is body on which projection is madeor operating on vector identifies argument type to f as “vector”function f(x) maps onto M means f over its domain is a surjectionwith respect to Mfunction f(x) over C means f evaluated at each and every element ofset Cinjective map or unique correspondence between setsfunction epigraphfunction domainfunction rangeR(A) the subspace: range of A , or span basis R(A) ; R(A) ⊥ N(A T )spanbasis R(A)as in spanA = R(A) = {Ax | x∈ R n } when A is a matrixovercomplete columnar basis for range of Aor minimal set constituting generators for vertex-description of R(A)or linearly independent set of vectors spanning R(A)