Glossary of Symbols

img “defined as”
img “denoted as”
img Exclude set B from set A, where B ⊂ A
img Kronecker product of matrices A and B
img Direct sum of set A and B
img A piece-wise function of x ≥ 0, which takes value z if x > 0, or max (z, 0) if x = 0
img The set of real numbers, n component real vectors, and n by n real matrices
img The set of nonnegative real numbers
img The set of complex numbers, n component complex vectors, and n by n complex matrices
img Space of functions which are n-times differentiable
img Curvature of a parametric curve at parameter ω
img The real part of complex number s
img The imaginary part of complex number s
img The open left half of the complex plane (briefly as LHP), img
img The closed left half of the complex plane (briefly as closed LHP), img
img The closed right half of the complex plane (briefly as RHP), img
img The open right half of the complex plane (briefly as open RHP), img
img The interior of the unit disc (briefly as IUD), img
img The closure of img (briefly as closed IUD), img
img The closed outer part of the unit disc (briefly as OUD), img
img The open outer part of the unit disc (briefly as open OUD), img
img The set of n by n transfer function matrices G(s), with ||G||∞< ∞
img The set of n by n rational transfer function matrices G(s), with ||G||∞< ∞
img Convex hull of elements r1 img, rn
img The set of integers from n1 to n2 satisfying n1 ≤ n2, {n1, img, n2}
img The index set of source nodes in a communication network, {1, 2, img, S}
img The index set of link nodes in a communication network, {1, 2, img, L}
img Transpose of matrix (vector) A
img Conjugate transpose of matrix (vector) A
j Unit of imaginary numbers, img
img img vector [1, img, 1]T
e1 n × 1 vector [1, 0, img, 0]T
img Diagonal matrix with diagonal entries img
img i-th eigenvalue of matrix img.
img Spectrum of matrix img
img Spectral radius of matrix img
img Maximum singular value of matrix img
img Rank of matrix A
img The space spanned by all the columns of matrix A
img The i-th column of matrix A
img The matrix formed by i1-th to i2-th columns of matrix A, where i1 ≤ i2
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