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In-Depth Information
Fig. 7.7
The effect of rotor
R
45
°
on vector
p
Similarly, reversing the product to
pR
45
°
we obtain
e
2
)
√
2
√
2
2
e
12
p
=
pR
45
°
=
(
e
1
+
2
−
√
2
2
√
2
2
√
2
2
√
2
2
=
e
1
−
e
2
+
e
2
+
e
1
√
2
e
1
=
asshowninFig.
7.7
.
Geometric algebra also employs a reversion function which reverses the sequence
of elements in a multivector by switching the signs of bivector and trivector ele-
ments. Instead of reversing the sequence of
p
and
R
β
, we can reverse
R
β
using
R
β
:
R
β
=
cos
β
−
sin
β
e
12
R
β
=
cos
β
+
sin
β
e
12
therefore,
√
2
2
+
√
2
2
e
12
(
e
1
+
p
=
R
†
45
°
p
=
e
2
)
√
2
2
√
2
2
√
2
2
√
2
2
=
e
1
+
e
2
−
e
2
+
e
1
√
2
e
1
=
and
e
2
)
√
2
√
2
2
e
12
p
=
pR
†
45
°
=
(
e
1
+
2
+
√
2
2
√
2
2
√
2
2
√
2
2
=
e
1
+
e
2
+
e
2
−
e
1
√
2
e
2
=
which means that
