v2009.01.01 - Convex Optimization

714 APPENDIX F. NOTATION AND A FEW DEFINITIONS
dB
EDM
S n 1
S n h
S n⊥
h
S n c
decibel
Euclidean distance matrix
subspace comprising all symmetric n×n matrices having all zeros in
first row and column (1878)
subspace comprising all symmetric hollow n×n matrices (0 main
diagonal), the symmetric hollow subspace (59)
orthogonal complement of S n h in Sn (60), the set of all diagonal matrices
subspace comprising all geometrically centered symmetric n×n
matrices; geometric center subspace S N ∆
c = {Y ∈ S N | Y 1=0} (1874)
S n⊥
c orthogonal complement of S n c in S n (1876)
R m×n
c
subspace comprising all geometrically centered m×n matrices
X ⊥ basis N(X T )
x ⊥ N(x T ) , {y | x T y = 0}
R(P ) ⊥ N(P T )
R ⊥ orthogonal complement of R⊆ R n ; R ⊥ ={y ∆ ∈ R n | 〈x,y〉=0 ∀x∈ R}
K ⊥
normal cone
K cone
K ∗
dual cone
K ◦ polar cone; K ∗ = −K ◦
K M+
K M
K λ
K ∗ λδ
H
monotone nonnegative cone
monotone cone
spectral cone
cone of majorization
halfspace