List of Symbols
R
Set of real numbers
R n
Set of n-dimensional vectors
x
= (x 1 , x 2 , . . . , x n ) T ∈ R n , vector in R n
x T
Transpose of vector x
M
= (m ij ) ∈ R n×m , n × m matrix
M T
Transpose of matrix
M −1
Inverse of matrix
det M
Determinant of matrix
trM
Trace of matrix
f (x)
: R → R, function of scalar variable x
f (x)
Derivative of f with respect to its argument x
f −1 (x)
Inverse function
f(x)
: R n → R m , vector function
J f
= (∂f i /∂x j ), Jacobian of f
∇f
= (∂f/∂x 1 , ∂f/∂x 2 . . . , ∂f/∂x n ) T , gradient of f (x) : R n →
R
j
=
√
−1
Re
Real part
Im
Imaginary part
∀
For all
∈
Is a member of
∩
Intersection
.
=
Definition
˙
x(t)
Derivative with respect to time t. The explicit notation
dx(t)/dt is also used
¨
x(t)
= d 2 x(t)/dt 2
ODE
Ordinary differential equation
DAE
Differential algebraic equation
SE
State equation
IVP
Initial value problem
EP
Equilibrium point
xxxi
R
Set of real numbers
R n
Set of n-dimensional vectors
x
= (x 1 , x 2 , . . . , x n ) T ∈ R n , vector in R n
x T
Transpose of vector x
M
= (m ij ) ∈ R n×m , n × m matrix
M T
Transpose of matrix
M −1
Inverse of matrix
det M
Determinant of matrix
trM
Trace of matrix
f (x)
: R → R, function of scalar variable x
f (x)
Derivative of f with respect to its argument x
f −1 (x)
Inverse function
f(x)
: R n → R m , vector function
J f
= (∂f i /∂x j ), Jacobian of f
∇f
= (∂f/∂x 1 , ∂f/∂x 2 . . . , ∂f/∂x n ) T , gradient of f (x) : R n →
R
j
=
√
−1
Re
Real part
Im
Imaginary part
∀
For all
∈
Is a member of
∩
Intersection
.
=
Definition
˙
x(t)
Derivative with respect to time t. The explicit notation
dx(t)/dt is also used
¨
x(t)
= d 2 x(t)/dt 2
ODE
Ordinary differential equation
DAE
Differential algebraic equation
SE
State equation
IVP
Initial value problem
EP
Equilibrium point
xxxi