Linear Systems

Symbol Description

∈	belongs to
R	field of real numbers
Rn	n-dimensional real Euclidean space
Rn × m	set of n × m real matrices
I	identity matrix
In	n × n identity matrix
XT	transpose of matrix X
P ≥ 0	symmetric positive semidefinite matrix P ∈ Rn × n
P > 0	symmetric positive definite matrix P ∈ Rn × n
P ≤ 0	symmetric negative semidefinite matrix P ∈ Rn × n
P < 0	symmetric negative definite matrix P ∈ Rn × n
P–1	the inverse of matrix P
rank(·)	rank of a matrix
trace(·)	trace of a matrix
‖ · ‖	Euclidean matrix norm
‖e‖2	L2-norm of signal e
L2[0,∞)	space of square integrable functions on [0, ∞)
l2[0,∞)	space of square summable infinite vector sequences over [0, ∞)
*	symmetric terms in a symmetric matrix