Thesis - Leigh Moody.pdf - Bad Request - Cranfield University

Glossary
_ _
0.14.2 Special Vectors
Zero and unity vectors are written as follows (in this example, for a 4vector),
0 ≡
4
1 ≡
4
( ) T
0 , 0 , 0 , 0
( ) T
1 , 1 , 1 , 1
The subscript defining the vector dimension may be omitted if it is obvious
from context.
0.14.3 Vector Partitioning
Row vector partitioning uses the following pro-forma,
( ( V ) M ( V ) ( V ) )
V : =
M
Column vector partitioning uses the following pro-forma,
V
X
xxxv
: =
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎝
V
V
Y
X
L
VY
L
Note that the subscripts (X,Y,Z) in these equations do not refer to Cartesian
components. Vector partitioning is not required when dealing with the
components of a vector.
0.14.4 Vector Jacobians
The column vector representing the partial derivative of a vector (Y) with
(m) elements with respect to a scalar (x) is,
∂ Y
∂ x
: =
⎛ ∂ y1
⎜
⎝ ∂ x
,
Z
L
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎠
,
∂ y
∂ x
The row vector representing the partial derivative of a scalar (y) with respect
to a vector (X) with (n) elements is,
∂ y
∂ X
: =
⎛ ∂ y
⎜
⎝ ∂ x1
, L
,
m
∂ y
∂ x
n
⎞
⎟
⎠
Z
T
⎞
⎟
⎠