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