Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

Appendix D 278
D.4 Coordinate transformations
I Multiplication of a vector by a matrix: x 0 = Ax
The multiplication of an -dimensional column vector x by an × matrix A gives a
new vector x 0 with components corresponding to those of x in a transformed coordinate
system.
I Example: Multiplication of a 2-dim vector
x =
µ
1
2
(D.34)
by a matrix
gives
µ
cos − sin
A =
sin cos
(D.35)
µ µ
cos − sin 1
Ax =
(D.36)
sin cos 2
µ
1 cos −
=
2 sin
(D.37)
1 sin + 2 cos
= x 0 (D.38)
I
Figure D.1: Rotation of a coordinate system.