v2010.10.26 - Convex Optimization

776 APPENDIX F. NOTATION AND A FEW DEFINITIONS∏ψ(Z)DDD T (X)D(X) TD −1 (X)D(X) −1D ⋆D ∗productsignum-like step function that returns a scalar for matrix argument(708), it returns a vector for vector argument (1579)symmetric hollow matrix of distance-square,or Euclidean distance matrixEuclidean distance matrix operatoradjoint operatortranspose of D(X)inverse operatorinverse of D(X)optimal value of variable Ddual to variable DD ◦ polar variable D∂√d ijd ijpartial derivative or partial differential or matrix of distance-squaresquared (1387) or boundary of set K as in ∂K (17) (24)(absolute) distance scalardistance-square scalar, EDM entryV geometric centering operator, V(D)= −V DV 1 2(996)V N V N (D)= −V T N DV N (1010)VN ×N symmetric elementary, auxiliary, projector, geometric centeringmatrix, R(V )= N(1 T ) , N(V )= R(1) , V 2 =V (B.4.1)V N N ×N −1 Schoenberg auxiliary matrix, R(V N )= N(1 T ) ,N(VN T )= R(1) (B.4.2)V X V X V T X ≡ V T X T XV (1187)