Mathematical Methods for Physicists: A concise introduction - Site Map

MATRIX ALGEBRA
Figure 3.1.
Coordinate changes by rotation.
space. In Fig. 3.1, the primed coordinates are obtained from the unprimed coordinates
by a rotation through an angle about the x 3 -axis. We see that x 0 1 is the
sum of the projection of x 1 onto the x 0 1-axis and the projection of x 2 onto the x 0 1-
axis:
similarly
and
x 0 1 ˆ x 1 cos ‡ x 2 cos…=2 † ˆx 1 cos ‡ x 2 sin ;
x 0 2 ˆ x 1 cos…=2 ‡ †‡x 2 cos ˆx 1 sin ‡ x 2 cos
We can put these in matrix form
x 0 3 ˆ x 3 :
X 0 ˆ R X;
where
0
X 0 B ˆ @
1
0
x1
0 x 1
x2
0 C B
A; X ˆ @ x 2
x3
0 x 3
1 0
1
cos sin 0
C B
C
A; R ˆ @ sin cos 0 A:
0 0 1
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